Chapter 11, Problem 28PT

To determine

To calculate: The time needed for Cleveland to do a job by himself.

Answer to Problem 28PT

The time required for Cleveland to do the work alone is $\frac{200}{3}$ minutes.

Explanation of Solution

Given information:

The required time for Sydney to paint a wall is $40\min$

The required time for Sydney and Cleveland to paint a wall is $25\min$

Calculation:

Consider the part of wall painted by Clevelane in x minutes $=1$

The part of wall painted by Cleveland in $1\min =\frac{1}{x}$

The part of wall painted by Sydney in $40\min$ minutes $=1$

The part of wall painted by Sydney in $1\min =\frac{1}{40}$

The part of wall painted by Sydney and Cleveland in $25\min$ minutes $=1$

The part of wall painted by Sydney and Cleveland in $1\min =\frac{1}{25}$

Form an equation based on the above information:

  $partofwal{l}_{Sydney}+partofwal{l}_{Cleveland}=partofwal{l}_{bothofthem}$

Substitute $\frac{1}{40}$ for $partofwal{l}_{Sydney}$ , $\frac{1}{x}$ for $partofwal{l}_{Cleveland}$ and $\frac{1}{25}$ for $partofwal{l}_{bothofthem}$

  $\begin{array}{c}\frac{1}{40}+\frac{1}{x}=\frac{1}{25}\\ \left(\frac{40+x}{40x}\right)25=1\\ \frac{40+x}{8x}\times 5=1\\ 5\left(40+x\right)=8x\end{array}$

Simplify the above equation to find the value of x .

  $\begin{array}{c}5\left(40+x\right)=8x\\ 200+5x=8x\\ 3x=200\\ x=\frac{200}{3}\end{array}$

Hence, the time required for Cleveland to do the work alone is $\frac{200}{3}$ minutes.