Chapter 9, Problem 1STP

To determine

To find: Which of the following rational equations can be solved for the number of minutes t it would take them to mow the lawn working together.

Answer to Problem 1STP

Correct option is (C)

Explanation of Solution

Given information:

Greg’s father can mow a lawn on his riding mower in 45 minutes and it takes Greg 1 hour 45 minute that is 105 minute to mow the lawn with a push mower.

Calculation:

Since, Greg’s father can mow a lawn on his riding mower in 45 minutes. Therefore,

The rate for Greg’s father is $\frac{1}{45}$ of a lawn per minute.

Also, it takes Greg 1 hour 45 minute that is 105 minute to mow the lawn with a push mower.

The rate for Greg is $\frac{1}{105}$ of a lawn per minute.

Let they take $t$ minute to complete it together. Therefore,

The combined rate is $\frac{1}{t}$ lawn per minute.

Thus,

  $\begin{array}{l}\frac{1}{45}+\frac{1}{105}=\frac{1}{t}\\ \frac{1}{45}\cdot t+\frac{1}{105}\cdot t=\frac{1}{t}\cdot t\\ \frac{t}{45}+\frac{t}{105}=1\end{array}$

Hence,

Correct option is (C)