Question

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

Answer 1

Answer:

3.6 hours = 3 hours 36 minutes

Step-by-step explanation:

Given :

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

To find :

total time taken to complete the work

Solution :

Let A can do the work in 6 hours.

In one hour, work done by A = 1/6

Let B can do the same work in 4 hours.

In one hour, work done by B = 1/4

In one hour, work done by A and B together:

  $\sf =\dfrac{1}{6}+\dfrac{1}{4} \\\\ \sf =\dfrac{2}{12}+\dfrac{3}{12} \\\\ \sf = \dfrac{2+3}{12} \\\\ \sf =\dfrac{5}{12}$

5/12 work is done by both A and B in 1 hour.

A has worked for 2 hours.

Work done by A in 2 hours = 2(1/6) = 1/3

The remaining work = 1 - 1/3

  = (3 - 1)/3

  = 2/3

A and B together complete the remaining work. Let time taken to complete the remaining work by them together be x hours.

5/12 work is done by both A and B in 1 hour.

2/3 work is done by A and B in x hours.

  $\sf x=\dfrac{\dfrac{2}{3}}{\dfrac{5}{12}} \\\\\\ \sf x=\dfrac{2}{3} \times \dfrac{12}{5} \\\\ \sf x=\dfrac{8}{5} \\\\ \sf x=1.6 \ hours$

Total time taken to complete the work = 2 hours + 1.6 hours = 3.6 hours