Chapter 7.8, Problem 7OE

To determine

Tofind:the total duration took by Joan alone to shovel the driveway.

Answer to Problem 7OE

Joanalone can take $3\frac{1}{3}$ to complete the work.

Explanation of Solution

Given:

Chuck can shovel the snow off his driveway in 40 min.

Joan and chuck both shovel the remaining snow in 10 min.

Concept used:

Rate of the work:

Ratio of work to the time interval with changes in time rate of work will change.

  $\text{work rate=}\frac{\text{work done}}{\text{time}}$ .

  $\text{work rate}\times \text{time=workdone}$ .

Calculation:

The work rate for chuck if he can shovel the driveway in $40$ minutes. He worked for $20$ minutes on his own and $10$ minutes.

Chuck’s work rate= $\frac{1}{40}$ .

Time: $20+10=30$ .

Work done:

  $\frac{\text{1}}{\text{40}}\left(\text{30}\right)\text{=}\frac{\text{3}}{\text{4}}$ .

Joan’s work for $10$ minutes the amount of work that she gets done is:

Time: $10$ minutes.

  $\text{Jaon}$ : $\frac{\text{1}}{\text{x}}\left(\text{10}\right)\text{=}\frac{\text{10}}{\text{x}}$ .

  $\frac{\text{40}}{\text{10}}\text{+}\frac{\text{10}}{\text{x}}\text{=1}$ .

  $\frac{\text{40x+100}}{\text{10x}}\text{=1}$ .

  $\text{40x+100=10x}$ .

  $\text{30x=100}$ .

  $\text{x=}\frac{10}{3}=3\frac{1}{3}$ .

Hence,Joanalone can take $3\frac{1}{3}$ to complete the work.