Question

Two men can do a piece of work in $6$ hours and $4$ hours respectively. After the first has worked for $2$ hours, he is joined by the other. By when should the work be completed.

Answer 1

Let the two men be A and B.

Given,

A can do a piece of work in $6$ hours and B in $4$ hours.

A's $1$ hour work $=\frac{1}{6}$

B's $1$ hour work $=\frac{1}{4}$

Both (A+B)'s $1$ hour work $=\frac{1}{6}+\frac{1}{4}=\frac{5}{12}$

After the $1$st (i.e. A) has worked for $2$ hours, he is joined by the other (i.e. B)

A's two hour work $=2\times \frac{1}{6}=\frac{1}{3}$

Remaining work $=1-\frac{1}{3}=\frac{2}{3}$

$\frac{5}{12}$ work is done by (A+B) in $1$ hour.

$\frac{2}{3}$ work is done by (A+B) in $\frac{12}{5}\times \frac{2}{3}=\frac{8}{5}$ hours

Total time taken to complete the work $=2+\frac{8}{5}$ hours

$=\frac{18}{5}$ hours $=3\frac{3}{5}$ hours $=3$ hours $+\frac{3}{5}\times 60$ minutes $=3$ hours $36$ minutes.

Hence, the work will complete in $3$ hours $36$ minutes.