Chapter 7.8, Problem 15P

To determine

Tofind:the duration of father to complete the work.

Answer to Problem 15P

It will take $\text{1}\frac{\text{2}}{\text{5}}$ hour amount of time father work by himself.

Explanation of Solution

Given:

It takes my father $3$ hour to plow the cornfield with his new tractor.

With old tractor it will take $5$ hours.

Lisa can do it in $\text{25 }$ 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 equation where $\text{x}$ is amount of time father work by himself.

  $\frac{\text{1+x}}{3}\text{+}\frac{1}{\text{5}}\text{=1}$ .

Combining like terms and subtracting $\frac{1}{5}$ from both side:

  $\frac{\text{1+x}}{\text{3}}\text{=}\frac{\text{4}}{\text{5}}$ .

Multiply both side by $3$ .

  $1+x=\frac{12}{5}$ .

Subtracting $1$ from both side:

  $\text{x=}\frac{\text{12}}{\text{5}}\text{-1=}\frac{\text{7}}{\text{5}}\text{=1}\frac{\text{2}}{\text{5}}$ .

Hence the it will take $\text{1}\frac{\text{2}}{\text{5}}$ houramount of time father work by himself.