Question

Two computers working together can finish a search in 40 seconds. One of these computers can finish in 60 seconds. How long would it take the second computer to finish the same search?

Answer 1

Let the time taken by 2nd computer be = x

Time taken by first computer = 60 seconds

Total time taken by both = 40 seconds

So, equation becomes:

$\frac{1}{60}+\frac{1}{x}=\frac{1}{40}$

$\frac{-1}{x}=\frac{1}{60}-\frac{1}{40}$

Solving this we get,

x=120 seconds

Hence, the 2nd computer will take 120 seconds to finish a search alone.

Answer 2

The second computer completes the search in 120 seconds.

SOLUTION:

Given, two computers working together can finish a search in 40 seconds.  One of these computers can finish in 60 seconds.  

So, work done by this computer in 1 second $=\frac{1}{60}$ [considering work as 1 unit ]

We have to find the time taken for the second computer to finish the same search.

Let the time taken by second computer be n seconds, then work done in 1 second $=\frac{1}{n}$

So, now, together in 1 second their work will be $\frac{1}{60}+\frac{1}{n}$

We are given that, it took 40 seconds to complete whole search,

$\text { Then, } 40 \times \text { work in one second }=\text { whole work } \rightarrow 40 \times\left(\frac{1}{60}+\frac{1}{n}\right)=1$

$\begin{array}{l}{\rightarrow \frac{1}{60}+\frac{1}{n}=\frac{1}{40}} \\\\ {\rightarrow \frac{1}{n}=\frac{1}{40}-\frac{1}{60}} \\\\ {\rightarrow \frac{1}{n}=\frac{60-40}{2400}} \\\\ {\rightarrow \frac{1}{n}=\frac{20}{2400}} \\\\ {\rightarrow \frac{1}{n}=\frac{1}{120}} \\\\ {\rightarrow n=120}\end{array}$