Answer:
Width 130 ft and
Length 320 ft
Step-by-step explanation:
We are given;
Length of the rectangular base is 70 ft less than three times the width;Perimeter of the rectangular base is 900 ftWe are required to determine the dimensions of the rectangular base;
Assuming the width of the rectangular base is x ft
Then length will be (3x - 70) ft
But;
Perimeter = 2L + 2W
Thus;
900 ft = 2(3x-70) + 2(x)
900 ft = 6x -140 +2x
1040 = 8x
x = 130
Thus;
Width = 130 ft
Length = 3x -70 = 320 ft
Hence the dimensions of the rectangular base are width 130 ft and length 320 ft
Question is in the problem, help please
Answer:
π units²
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ← r is the radius
Here diameter d = 2, thus r = 2 ÷ 2 = 1, thus
A = π × 1² = π × 1 = π units² ← exact solution
or A = 3.14 units² ← as a decimal
Elle is buying new flooring for her kitchen
and laundry room. She knows that the
area of the kitchen is 132 square feet. The
laundry room is 8 1/3 feet by 6 3/4 feet. What is
the total area of the two rooms?
Answer:
The total area of the two rooms is 188.25 square feet
Step-by-step explanation:
Given:
Area of the kitchen = 132 square feet.
Dimension of the Laundry room = 8 1/3 feet by 6 3/4 feet.
To Find:
The total area of the two rooms = ?
Solution:
Area of the two rooms = Area of the kitchen + Area of the laundry room
Area of the two rooms = 132 + Area of the laundry room
Area of the laundry room =[tex](8 \frac{1}{3}) \times (6 \frac{3}{4})[/tex]
Area of the laundry room =[tex]\frac{25}{3} \times \frac{27}{4}[/tex]
Area of the laundry = [tex]\frac{675}{12}[/tex]
Area of the two rooms = [tex]132 + \frac{675}{12}[/tex]
Area of the two rooms = 132 + 56.25
Area of the two rooms = 188.25 square feet
Final answer:
The total area of Elle's kitchen and laundry room combined is 188.25 square feet. This is found by first calculating the area of the laundry room with given dimensions and then adding it to the area of the kitchen.
Explanation:
The question involves finding the total area of two rooms, given the area of one and the dimensions of the other. The kitchen has an area of 132 square feet. For the laundry room, we need to calculate the area by multiplying its length and width. The dimensions are 8 1/3 feet by 6 3/4 feet. To find the area, convert mixed numbers to improper fractions: 8 1/3 becomes 25/3 feet, and 6 3/4 becomes 27/4 feet. The area is then calculated as (25/3) * (27/4) square feet.
To compute this, multiply the numerators and denominators separately: (25*27) / (3*4) = 675 / 12, which simplifies to 56.25 square feet. Now, add the area of the laundry room to the area of the kitchen to get the total area of both rooms: 132 + 56.25 = 188.25 square feet. Therefore, the total area of the two rooms is 188.25 square feet.
A class will have 1 test and 5 homework assignments to complete. If the test is worth 80 points and each homework assignment is work 25% of the test, how many points may be earned during this unit?
Answer:
180 points.
Step-by-step explanation:
Given:
A class will have 1 test and 5 homework assignments to complete.
The test is worth 80 points.
Each homework assignment is work 25% of the test.
Question asked:
How many points may be earned during this unit ?
Solution:
By unitary method:
Points may be earned from 1 assignments = [tex]25\% of 80[/tex] (given)
= [tex]\frac{25}{100} \times 80 = \frac{2000}{100} = 20[/tex]
Points may be earned from 5 assignments = [tex]5\times 20 = 100[/tex]
Points may be earned from 1 test = [tex]80[/tex]
Total points may be earned = 100 + 80 = 180
Therefore, 180 points may be earned during this unit.
Questiul 4 15 points)
Laurie and Maya sold at most $50 worth of get-well and friendship cards. The
friendship cards, x, were sold for $2 each and the get-well cards, y, were sold for
$1.50 each. Which point represents a reasonable number of cards sold?
Answer:
2 dollars cuz ur poor
Step-by-step explanation:
SHOW ALL WORK: Graph each lineby plotting its intercepts or by using the y intercept and slope. {2x-y=4 {3y-3x=6
Answer:
x-y=-2
Step-by-step explanation:
Divide both sides if the equations by 3.
(3y-3x)÷3=6÷3
y-3x÷3=2
calculate the quotient
y-x=2
multiply both sides of the equation bub -1
-1x(-x)-1y=-1x2
any expression multiplied by -1
x-1y=-1x2
any expression multiplied by 1 remains the same.
x--y=-1x2
x-y=-2
How many times can 27 go into 224
What is the value of the function FX equals 4X +9 when X equals
In a triangle, one angle measures 68° and another
angle measures 38°. What is the measure of the third
angle?
Answer:
74°
Step-by-step explanation:
all angles of a triangle will always end up equal to 180°
68 + 38 = 106
180 - 106 = 74
What is 2 = f - 27.
Answer:
F=29
Step-by-step explanation:
27+2
Answer:
f=29
Step-by-step explanation:
Lesson 12 Homework
A rectangular garden has a total area of 48 square yards. Draw and label two possible rectangular
gardens with different side lengths that have the same area.
on the fifth figure in
See picture for solution to your problem.
How many times can 27 go into 224
Answer:
27 can go into 224 8 times by dividing 224 by 27 .
2453 minus 249 equals
Answer: 2,204
Step-by-step explanation:
Final answer:
To solve 2453 minus 249, align the numbers by place value and subtract each column starting from the rightmost digit, borrowing where necessary. The result of 2453 minus 249 is 2204.
Explanation:
The question is a basic arithmetic problem involving subtraction. The task is to subtract 249 from 2453. We write the numbers in column form, aligning the units, tens, hundreds, and thousands places properly:
2453
- 249
------
We start subtracting from the rightmost digit (units place) and proceed to the left:
Finally, subtract in the thousands place: 2 minus 0 is 2.
After completing the subtraction, we have the result:
2204
Therefore, 2453 minus 249 equals 2204.
Nara multiplied two whole numbers together to equal a product of 90.
Then she accidentally spilled ketchup on her work.
Select the three responses below that could be one of the numbers Nara multiplied.
Answer:
30×3=90 10×9=90 45×2=90 . .
Answer: 5, 10, 18
Step-by-step explanation:
9. A relation contains the points ( -5,-10),( -2,-4)(-1,-2),(4,8) and (5,10) . Is this a function? Explain. (2 points)
Answer:
Yes it is a function given by f(x) = 2x
Step-by-step explanation:
Any function can approximated as series or a polynomial. For example,
[tex]e^{x} = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} ...[/tex] (exponential function)
(n! or n factorial is equal to n(n-1)(n-2)...3.2.1 ; 3! = 3.2.1 = 6)
and for the series to converge(the sum does not go to infinity), higher order terms must tend to zero.
General form of a polynomial/series: [tex]f(x) = a + bx +cx^{2} + ...[/tex]
For the given set of points, we can start with the straight line equation:
[tex]f(x) = y = a + bx[/tex] ........(1)
Let us take two points from the given relation: (-5, -10), (-1, -2)
and put the respective x and y values in equation (1), we get two equations, which we can then solve simultaneously to get values of [tex]a[/tex] and [tex]b[/tex]:
[tex]-10=a-5b[/tex] ........(2)
[tex]-2=a-b[/tex] ..........(3)
Now (3) - (2) gives us: [tex]b=2[/tex] and putting the value of [tex]b[/tex] in any of the above equation gives us [tex]a=0[/tex]
Hence, we get the equation, [tex]f(x)=y=2x[/tex]
It can be seen that all the given points satisfies this relation and since we get a unique [tex]y[/tex] for every [tex]x[/tex], we can call this a function.
Final answer:
The provided relation is a function because each x-value is unique and maps to exactly one y-value, fulfilling the criterion that every element of the domain is associated with exactly one element of the range.
Explanation:
The question asks if a relation containing the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10) is a function. To determine if this relation is a function, we need to examine if any x-value (the first number in each pair) repeats with a different y-value (the second number in each pair). Upon inspection, we see that each x-value is unique to a single y-value, which means that each element of the domain maps to a unique value in the range. Therefore, we can conclude that this relation is indeed a function.
In general, a function is defined as a relation in which every element of the domain (set of all first elements) is associated with exactly one element of the range (set of all second elements). This criterion is met in the relation provided as each x-value is unique and paired with only one y-value.
Suppose h(t)= -0.2 + 2t models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds
The maximum height of the ball is found at 64 feet
Explanation:Hello! remember to write complete and clear questions in order to get good and exact answers. I've found a similar question so I have written it in a comment above. We know that h(t) models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds. This equation follows a quadratic function so from math we know that the maximum or minimum of this type of functions is found at the vertex of its graph. So:
[tex]f(x)=ax^2+bx+c \\ \\ \\ Vertex \ (h,k): \\ \\ h=-\frac{b}{2a} \\ \\ k=f(-\frac{b}{2a}) \\ \\ \\ Our \ function \ is: \\ \\ h(t)=-16t^2+64t \\ \\ \\ Comparing: \\ \\ a=-16 \\ \\ b=64 \\ \\ c=0 \\ \\ \\ h=-(\frac{64}{2(-16)})=2 \\ \\ k=-16(2)^2+64(2) \\ \\ k=64[/tex]
Finally, the maximum height of the ball is found at 64 feet
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Volume of a box: https://brainly.com/question/10501080
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WILL GIVE BRAINLIEST!?!?!!?!?!? WHATS 9+10?????
Write an expression with two terms. 1 term should have a coefficient with a variable and the other term should be constant. Name the coefficient, the variable, and the constant in the expression. Then write a word phrase for your expression.
________________________________________________________________________________________________________________________________________
Answer:
y = 2x + 5
Step-by-step explanation:
The 2 would be the coefficient with x as a variable, and the 5 would be the constant.
At the beginning of the day Jessica had 5 dollars (constant), and for every hour she worked (variable), she made 2 dollars (coefficient).
An example of an expression with two terms is 3x + 5, where 3 is the coefficient, x is the variable, and 5 is the constant. A word phrase for this expression is "Three times a number plus five."
An example of an expression with two terms where one term has a coefficient with a variable and the other term is constant is:
3x + 5
In this expression:
The coefficient is 3.
The variable is x.
The constant is 5.
A word phrase for this expression could be: "Three times a number plus five."
She gave 1/3 of cookies for her husband 1/4 of the cookies to her son and 1/6 of a cookies to her neighbor she ate the remaining six cookies how many cookies did she make
She made 15 cookies
Solution:
Let "x" be the number of cookies she made
She gave 1/3 of cookies for her husband
Therefore,
[tex]Husband = \frac{1}{3}x[/tex]
Find the remaining
[tex]Remaining = x - \frac{x}{3} = \frac{3x-x}{3} = \frac{2x}{3}[/tex]
1/4 of the cookies to her son
Therefore,
[tex]son = \frac{1}{4} \times \frac{2x}{3} = \frac{x}{6}[/tex]
Now again find the remaining
[tex]Remaining = \frac{2x}{3} - \frac{x}{6} = \frac{x}{2}[/tex]
1/6 of a cookies to her neighbor
[tex]Neighbor = \frac{1}{6} \times \frac{x}{2} = \frac{x}{12}[/tex]
Now again find the remaining
[tex]Remaining = \frac{x}{2} - \frac{x}{12} = \frac{5x}{12}[/tex]
She ate the remaining six cookies
Therefore,
[tex]\frac{5x}{12} = 6\\\\5x = 72\\\\x = 14.4[/tex]
Thus she made approximately 15 cookies
Maddy made $22.50 for babysitting for 5 hours for her aunt. Maddy was paid $21.00 for 3.5 hours of babysitting for her neighbor. How much more per hour does Maddy’s neighbor pay than her aunt?
Answer:Her Aunt paid her 4.50 and hour and her neighbor 6 an hour. The difference is 1.5
Step-by-step explanation:
Find the value of x and explain please
ANSWER ASAP!!!!!!!!!!!!!!!!!
Answer:
y = - 4
Step-by-step explanation:
Given
y = 2 - 9x ← substitute x = [tex]\frac{2}{3}[/tex]
y = 2 - ( 9 × [tex]\frac{2}{3}[/tex] ) ← cancel the 9 and 3 by 3
= 2 - (3 × 2 )
= 2 - 6
= - 4
4√6 •√3 how do I show work for this because the answer is 2√12
Answer:
[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]
Step-by-step explanation:
We want to simplify the radical expression:
[tex]4 \sqrt{6} \times \sqrt{3} [/tex]
We write √6 as √(2*3).
This implies that:
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2 \times 3} \times \sqrt{3} [/tex]
We now split the radical for √(2*3) to get:
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times \sqrt{3} \times \sqrt{3} [/tex]
We obtain a perfect square at the far right.
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times (\sqrt{3} )^{2} [/tex]
This simplifies to
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times 3[/tex]
This gives us:
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \times 3 \sqrt{2} [/tex]
and finally, we have:
[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]
Solve this equation 3x4x4x15-14+1= ?
Answer:
my answer is 707
Step-by-step explanation:
i used a calculator lol
Answer:
707
Step-by-step explanation:
I need help with this asap.
4a, b, c
From this problem, we know that during the weekend Fiona bought some frozen seafood at the market. She bought the following things:
A large tray of sardinesA 3 kg bag of squidA 2kg box of musselsLet:
x: The large tray of sardines
y: The 3 kg bag of squid
z: The 2kg box of mussels
Then, we have the following information:
The sardines and the squid cost €50:
[tex]x+y=50 \ ... \ eq1[/tex]
The sardines and the mussels cost €43:
[tex]x+z=43 \ ... \ eq2[/tex]
The squid and the mussels cost €26:
[tex]y+z=26 \ ... \ eq3[/tex]
Isolating x from eq 1 and substituting into eq 2:
[tex]From \ eq1: \\ \\ x=50-y \\ \\ \\ Substituting \ into \ eq2: \\ \\ (50-y)+z=43 \\ \\ -y+z=43-50 \\ \\ -y+z=-7 \ ... \ eq4[/tex]
Adding eq3 and eq4:
[tex]\ \ y+z=26 \\ \\ -y+z=-7 \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\ 2z=19 \\ \\ z=9.5[/tex]
From eq 3:
[tex]y+z=26 \\ \\ y+9.5=26 \\ \\ y=26-9.5 \\ \\ y=16.5[/tex]
From eq 1:
[tex]x=50-y \\ \\ x=50-16.5 \\ \\ x=33.5[/tex]
Finally:
A large tray of sardines cost €33.5A 3 kg bag of squid cost €16.5A 2kg box of mussels cost €9.5Learn more:Solving systems of linear equations: https://brainly.com/question/13799715
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What is the answer to this equation
3 3/7 + 4 5/7=
Answer:
8 1/7Step-by-step explanation:
First,you take 3 and 3/7 and line it up with 4 and 5/7 and first you add your whole numbers which come before the fractions and get 7.Next,you add the fractions and get 8/7. Now you know it needs symplified because its an improper fraction. To symplify you have to × or ÷ and whatever one you do you have to do it to both the numerator and denominator. If you divide 8÷7=1 R1 7÷7=1. Last add 7+1+1/7=8 1/7.
What is the radius of a
cylinder with a diameter of
36?
Answer:
radius=diameter÷2=36÷2=13
Yo sup??
diameter=2*radius
36=2 r
r=18
therefore the radius is 18 units
Hope this helps
Use the distributive property to create an equivalent expression to 7x divided by 56 use GCF
Answer:
x/8
Step-by-step explanation:
7x/56=x/8
What is the answer to this 4×3^2?
Evaluate the expression.
Answer:
36
Step-by-step explanation:
The first thing to simplify is the Exponents
3^2 means 3 multiplied by it self 2 times
3×3=9
4×3^2
4×9
36
can someone help me one the questions I have not answered?
Answer:
[tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex] 391 = 17×23391 is not a Prime NumberExplanation:
391[tex]391\:\mathrm{divides\:by}\:17\quad \:391=23\cdot \:17[/tex]
[tex]=17\cdot \:23[/tex]
17, 23 are all prime number. So no further factorization possible
[tex]=17\cdot \:23[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}391:\quad 17,\:23[/tex] 391 = 17×23391 is not a Prime Number Q # 3Answer:
[tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]291 = 3×97291 is not a Prime NumberExplanation:
291[tex]291\:\mathrm{divides\:by}\:3\quad \:291=97\cdot \:3[/tex]
[tex]=3\cdot \:97[/tex]
3, 97 are all prime number. So no further factorization possible
[tex]=3\cdot \:97[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}291:\quad 3,\:97[/tex]291 = 3×97291 is not a Prime Number Q # 4Answer:
[tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]37=37Yes, 37 is a Prime NumberExplanation:
3737 is a prime number. So no further factorization possible
[tex]=37[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}37:\quad 37[/tex]37=37Yes, 37 is a Prime Number Q # 6Answer:
[tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]411 = 3×137 411 is not a Prime NumberExplanation:
411[tex]411\:\mathrm{divides\:by}\:3\quad \:411=137\cdot \:3[/tex]
[tex]=3\cdot \:137[/tex]
3, 137 are all prime number. So no further factorization possible
[tex]=3\cdot \:137[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}411:\quad 3,\:137[/tex]411 = 3×137 411 is not a Prime Number Q # 7Answer:
[tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]387 = 3×3×43387 is not a Prime NumberExplanation:
387[tex]387\:\mathrm{divides\:by}\:3\quad \:387=129\cdot \:3[/tex]
[tex]=3\cdot \:129[/tex]
[tex]129\:\mathrm{divides\:by}\:3\quad \:129=43\cdot \:3\\=3\cdot \:3\cdot \:43[/tex]
3, 43 are all prime number. So no further factorization possible
[tex]=3\cdot \:3\cdot \:43[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}387:\quad 3,\:43[/tex]387 = 3×3×43387 is not a Prime Number Q # 9Answer:
[tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]113 = 113Yes, 113 is a Prime NumberExplanation:
113113 is a prime number. So no further factorization possible
[tex]=113[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}113:\quad 113[/tex]113 = 113Yes, 113 is a Prime Number Q # 16Answer:
[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]293 = 293 Yes, 293 is a Prime NumberExplanation:
293
[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]
[tex]=293[/tex]
[tex]293\mathrm{\:is\:a\:prime\:number,\:therefore\:no\:factorization\:is\:possible}[/tex]
[tex]=293[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]293 = 293 Yes, 293 is a Prime Number Q # 17Answer:
[tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]451=11×41 451 is not a Prime NumberExplanation:
451[tex]451\:\mathrm{divides\:by}\:11\quad \:451=41\cdot \:11[/tex]
[tex]=11\cdot \:41[/tex]
11, 41 are all prime number. So no further factorization possible
[tex]=11\cdot \:41[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}451:\quad 11,\:41[/tex]451=11×41 451 is not a Prime Number Q # 18Answer:
[tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]459 = 3×3×3×17459 is not a Prime NumberExplanation:
459[tex]459\:\mathrm{divides\:by}\:3\quad \:459=153\cdot \:3[/tex]
[tex]=3\cdot \:153[/tex]
[tex]153\:\mathrm{divides\:by}\:3\quad \:153=51\cdot \:3[/tex]
[tex]=3\cdot \:3\cdot \:51[/tex]
[tex]51\:\mathrm{divides\:by}\:3\quad \:51=17\cdot \:3[/tex]
[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]
3, 17 are all prime number. So no further factorization possible
[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}459:\quad 3,\:17[/tex]459 = 3×3×3×17459 is not a Prime Number Q # 19Answer:
[tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]385 = 5×7×11385 is not a Prime NumberExplanation:
385[tex]385\:\mathrm{divides\:by}\:5\quad \:385=77\cdot \:5[/tex]
[tex]=5\cdot \:77[/tex]
[tex]77\:\mathrm{divides\:by}\:7\quad \:77=11\cdot \:7[/tex]
[tex]=5\cdot \:7\cdot \:11[/tex]
5, 7, 11 are all prime number. So no further factorization possible
[tex]=5\cdot \:7\cdot \:11[/tex]
So,
[tex]\mathrm{Prime\:factors\:of\:}385:\quad 5,\:7,\:11[/tex]385 = 5×7×11385 is not a Prime Number Q # 20Answer:
[tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]162 = 2×3×3×3×3 162 is not a Prime NumberExplanation:
162[tex]162\:\mathrm{divides\:by}\:2\quad \:162=81\cdot \:2[/tex][tex]=2\cdot \:81[/tex][tex]81\:\mathrm{divides\:by}\:3\quad \:81=27\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:27[/tex][tex]27\:\mathrm{divides\:by}\:3\quad \:27=9\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:9[/tex][tex]9\:\mathrm{divides\:by}\:3\quad \:9=3\cdot \:3[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex][tex]2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex][tex]=2\cdot \:3\cdot \:3\cdot \:3\cdot \:3[/tex]So,
[tex]\mathrm{Prime\:factors\:of\:}162:\quad 2,\:3[/tex]162 = 2×3×3×3×3 162 is not a Prime NumberKeywords: prime factor
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Plz help now for 30 points k
Find total of non blue socks:
7 + 8 + 4 = 19
There are 9 blue socks.
Ratio is blue / non blue = 9/19
Anton's family drove 216 mi to the lake averaging 48 mi/h . On the return trip home they averaged 54 mi/h .
What was the total time that Anton's family spent driving to and from the lake?
The total time that Anton's family spent driving to and from the lake is 8.5 hours
Solution:
Time taken is given by formula:
[tex]Time = \frac{distance}{speed}[/tex]
Anton's family drove 216 mi to the lake averaging 48 mi/h
⇒ Anton's family drove total distance = 216 mi les
⇒ Speed of Antony's family driving to lake = 48 miles per hour
[tex]Time = \frac{216}{48} = 4.5[/tex]
Therefore, time taken to drive to lake is 4.5 hour
On the return trip home they averaged 54 mi/h
[tex]Time = \frac{216}{54} = 4[/tex]
Therefore, time taken to return home is 4 hours
Total time = 4.5 + 4 = 8.5 hours
Thus the total time that Anton's family spent driving to and from the lake is 8.5 hours