Q. 28 PT - Algebra 1

Question

PAINTING 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?

Step-by-Step Solution

Answer

It will take $\frac{200}{3}$ minutes for Cleveland to paint the wall.

Step 1. Write.

Write the given equation in terms of equation.

Let $x$ be the number of minutes Cleveland take to paint the wall, such that,

$\frac{1}{40}+\frac{1}{x}=\frac{1}{25}$

Step 2. Multiplication.

Multiply numerator and denominator of $\frac{1}{40}$ by $x$ and multiply numerator and denominator of $\frac{1}{x}$ by 40.

$\frac{1\cdot x}{40\cdot x}+\frac{1\cdot 40}{x\cdot 40}=\frac{1}{25}$

Step 3. Simplify.

Simplify the above obtained equation.

$\begin{array}{c}\frac{x}{40x}+\frac{40}{40x}=\frac{1}{25}\\ \frac{40+x}{40x}=\frac{1}{25}\\ 25\left(40+x\right)=40x\\ 1000+25x=40x\\ 1000=15x\\ x=\frac{1000}{15}\\ =\frac{200}{3}\end{array}$

Therefore, it will take $\frac{200}{3}$ minutes for Cleveland to paint the wall.