Chapter 7.8, Problem 12P

To determine

Tofind:the total duration stan brother can load the truck alone.

Answer to Problem 12P

Stan’s brother will take $40$ minutes to load the truck alone.

Explanation of Solution

Given:

Stan can load his truck in $24$ min.

If his brother helps him it takes $15$ min to load the truck.

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 equation where $\text{x}$ is the time it takesStan’s brother to load the truck alone.

  $\frac{\text{15}}{\text{24}}\text{+}\frac{\text{15}}{\text{x}}\text{=1}$ .

Combining like terms and simplifying the fraction:

  $\text{5x+120=8x}$ .

Subtracting $\text{5x}$ from both side:

  $\text{120=3x}$ .

Dividing both side by $3$ :

  $\text{x=40}$ .

Hence Stan’s brother will take $40$ minutes to load the truck alone.