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# Math

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Emily just finished painting the smallest wall in her room. It took her 1 hour and 40 minutes and she was able to paint at a rate of forty-two square feet per hour. If the wall is thirteen feet long, how tall is it? Round your answer to the nearest foot.

Jan 5, 2022

#1
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Suppose the wall is x feet tall.

Given the wall is  13 feet long.

Find the area of the wall :

The area is

13

× x = 13x2

42 feet2 is painted by 1 hour.

So, 13x

feet2 will be painted 13x/42 hour i.e

{(13x)×60}/42 minutes i.e 390x/21 minutes.

By given condition ,

390x/21 minutes = 1 hour 40 minutes = 100 minutes.

I.e 390x = 2100

I.e x= 2100/390=210/39 = 5.38

Therefore the wall is 5 .38 feet tall.

Jan 6, 2022
#2
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First, calculate the total area of the wall.

1 hour and 40 minutes is equivalent to 1 2/3 hours or 5/3 hrs.

if her rate was 42 ft2/hr, then the total area she painted

was

A = 42 * 5/3 = 70 ft2

Now, the formula to find the area of the wall is

A = Lw

Let A = 70 and, L = 13 and w be the height of the wall. So,

A = Lw

70 = 13w

13w/13 = 70/13

w ≈ 5

Hence, the height of the wall is approximately 5 feet tall.

Jan 6, 2022