Sydney can paint a 60 square foot wall in 40 minutes. Working with her friend Cleveland, the two of them can paint the wall in 25 minutes. How long would it take Cleveland to do the job himself?

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09-09-2016
Mathematics

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Sydney can paint a 60 square foot wall in 40 minutes. Working with her friend Cleveland, the two of them can paint the wall in 25 minutes. How long would it take Cleveland to do the job himself?

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abbusaicharan02 abbusaicharan02 · Answer 1 · 2022-05-14T13:48:49+02:00

The time taken by Cleveland to do the job himself is [tex]\dfrac{10}{9}[/tex] hours.

Work problem

Work issues are word problems in which several persons collaborate on a task but work at various speeds.

How to find the time?

Let us assume the time taken by Cleveland is [tex]\dfrac{1}{t}[/tex].

It is given that Sydney can paint a 60 square foot wall in 40 minutes. and working with her friend Cleveland, the two of them can paint the wall in 25 minutes.

Then we can write

[tex]\dfrac{1}{40} +\dfrac{1}{t} =\dfrac{1}{25}\\\dfrac{1}{t}=\dfrac{1}{25}-\dfrac{1}{40}\\\dfrac{1}{t}=\dfrac{40-25}{40\times 25}\\\dfrac{1}{t}=\dfrac{3}{200}[/tex]

By Solving it further, we will get

[tex]t=\dfrac{200}{3}[/tex] minutes.

Converting it in hours, we will be

[tex]t=\dfrac{200}{3\times 60}\\t=\dfrac{10}{9}[/tex]

So, the time taken by Cleveland to do the job himself is [tex]\dfrac{10}{9}[/tex] hours

Learn more about the time taken here- https://brainly.com/question/3386488

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