Chapter 11.5, Problem 13P

It takes you about an hour to make one batch of cookie dough and your brother about 42 minutes to make one batch. How much time does it take, you to make a batch of cookie dough together?

To determine

To calculate the time taken to make a batch of cookie dough together.

Answer to Problem 13P

The time taken for making the cookie dough together is $25\frac{5}{7}$ minutes.

Explanation of Solution

Given information:

The given statement is:

“It takes you about an hour to make one batch of cookie dough and your brother about $42$ minutes to make on batch. How much time does it take you to make a batch of cookie dough together?”

Calculation:

Work done in making the batch of cookie dough in one hour is $\frac{1}{60}$ .

Work done in making the batch of cookie dough in $42$ minutes is $\frac{1}{42}$ .

The work done together can be calculated by:

  $\begin{array}{l}\frac{1}{60}+\frac{1}{45}\\ =\frac{3+4}{180}\\ =\frac{7}{180}\end{array}$

The time taken to make the batch of cookie dough together is:

  $\begin{array}{l}1÷\frac{7}{180}\\ =1\times \frac{180}{7}\\ =\frac{180}{7}\\ =25\frac{5}{7}\end{array}$

Hence, the time taken for making the cookie dough together is $25\frac{5}{7}$ minutes.