Question

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

Answer 1

Step-by-step explanation:

Let " A " be the first man, and " B " be the second man.

A can do a piece of work in 6 hours

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

B can do the work in 4 hours

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

(A + B)'s 1 day work = $\dfrac{1}{6} + \dfrac{1}{4}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{2 + 3}{12}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{5}{12}$

Given, After the first person has worked for 2 hours, he is joined by the other.

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

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

5/12 of the work is completed by A and B in 1 hour

2/3 of the work in completed in $\dfrac{12}{5} \times \dfrac{2}{3} = \dfrac{8}{5}$

Remaining work is completed by both in $\dfrac{8}{5}$ hours

Time taken to complete the whole work

= $2 + \dfrac{8}{5}$

= $\dfrac{10 + 8}{5}$

= $\rm \dfrac{18}{5} = 3 hours \: 36 minutes$

∴ Total work is completed in 3hours 36minutes