Chapter 11, Problem 26CR

To determine

Find the time taken by the old photocopier to make 72 copies working alone.

Answer to Problem 26CR

The older photocopier can make 72 copies in 6 minutes.

Explanation of Solution

Given:

A new photocopier can make 72 copies in 2 min. When an older photocopier is operational, the two photocopiers together can make 72 copies in 1.5 min. How long would it take the older photocopier to make 72 copies working alone?

Concept Used:

Let x be the rate of the old photocopier.

Find the rate (copies/ minute) for new photocopier and rate for together.

Rate (copies per minute) of new photocopier + Rate (copies per minute) of old photocopier = Rate of together.

Calculation:

Let x be the rate of the old photocopier.

The rate of the new photocopier is 72 copies in 2 minutes or $\frac{72}{2}=36$ copies per minute.

Together, their total rate in 72 copies in 1.5 minutes or $\frac{72}{1.5}=48$ copies per minute.

Rate (copies per minute) of new photocopier + Rate (copies per minute) of old photocopier = Rate of together.

The equation: $36+x=48$

  $\begin{array}{l}36+x=48\\ 36-36+x=48-36[\text{Subtract}36\text{from}\text{both}\text{sides}]\\ x=12\end{array}$

The rate of the photocopier is 12 copies per minute.

Therefore, it can make 72 copies in: $72\text{copies}·\frac{\text{1}\text{minute}}{\text{12}\text{copies}}=\text{6}\text{minutes}$

Thus, the older photocopier can make 72 copies in 6 minutes.