Chapter 5.9, Problem 3ST

To determine

Find how long would it take both computers to do the processing.

Answer to Problem 3ST

  $3\frac{1}{3}$ hours

Explanation of Solution

Given:

One computer can process a payroll in $6\text{h}$ . An older computer can do the same job in $7\text{h}30\text{min}$ .

Calculation:

Let both the computers can do the processing together in t hours.

Let the whole work = 1

One computer does processing alone in 6 hours.

So, in 1 hour , the processing it does = $\frac{1}{6}$

So, in t hours , the processing it does = $\frac{\mathrm{t}}{6}$ .....................(1)

The old computer does processing alone in 7.5 hours.

So, in 1 hour, the processing it does = $\frac{1}{7.5}$

So, in t hours , the processing it does = $\frac{\mathrm{t}}{7.5}$ ...................(2)

So, both the computers together complete work in t hours = $\frac{\mathrm{t}}{6}+\frac{\mathrm{t}}{7.5}$

and the whole work is 1.

So,

  $\begin{array}{l}\frac{\mathrm{t}}{6}+\frac{\mathrm{t}}{7.5}=1\\ \Rightarrow 7.5\mathrm{t}+6\mathrm{t}=7.5(6)\mathrm{...................}[\text{multiply each side by 7}\text{.5(6)]}\\ \Rightarrow 13.5\mathrm{t}=45\\ \Rightarrow \mathrm{t}=\frac{45}{13.5}\mathrm{...........................}[\text{divide each side by 13}\text{.5]}\\ \Rightarrow \mathrm{t}=3\frac{1}{3}\text{ hours}\end{array}$

So, both the computers do processing in $3\frac{1}{3}$ hours.