Chapter 11.5, Problem 14P

Your dad can clean the house in 2 hours and 10 minutes. Your mom can clean it in an hour and 45 minutes. How many hours does it take them to clean the house if they work together?

To determine

To calculate the time taken to clean the house together.

Answer to Problem 14P

The time taken for cleaning the house together is $58\frac{4}{47}$ minutes.

Explanation of Solution

Given information:

The given statement is:

“Your dad can clean the house in $2$ hours and $10$ minutes. Your mom can clean it in an hour and $45$ minutes. How many hours does it take them to clean the house if they work together?”

Calculation:

Time taken by dad to clean the house is $2$ hours and $10$ minutes or $130$ minutes.

Work done by dad is $\frac{1}{130}$ .

Time taken by mom to clean the house is an hour and $45$ minutes or $105$ minutes.

Work done by mom is $\frac{1}{105}$ .

The work done together can be calculated by:

  $\begin{array}{l}\frac{1}{130}+\frac{1}{105}\\ =\frac{21+26}{2730}\\ =\frac{47}{2730}\end{array}$

The time taken for cleaning the house together is:

  $\begin{array}{l}1÷\frac{47}{2730}\\ =1\times \frac{2730}{47}\\ =\frac{2730}{47}\\ =58\frac{4}{47}\end{array}$

Hence, the time taken for cleaning the house together is $58\frac{4}{47}$ minutes.