Question

one man can do a piece of work in 3 hours, another can do the same piece of work in 2 hours. How long will they take if theywork together?

Answer 1

1st man 1 hour work = 1/3 hour
2nd man 1 hour work = 1/2
Now if they work together
Let the time be x hour
1x/3+1x/2=1
5x/6=1
X =6/5hour

Answer 2

The total taken by both them to complete the work = 2.2hrs

Given:

One man can do a piece of work in 3 hours

Another man can do the same piece of work in 2 hours

To find:

How long will they take if they work together?

Solution:

Given One man can do a piece of work in 3 hours

The work can be done in 1 hr = 1/3

Another man can do the same piece of work in 2 hours  

The work can be done by 2nd man in 1 hr = 1/2

Therefore,

The work can be done by both of them in 1hr = 1/3+1/2 = 5/6

The remaining work will be = 1- 5/6 = 1/6

Assume that both of them completed the 1/6 of work in x hrs

⇒ the work can be done in x hrs = x(1/6) = x/6

We know that total work will be equal to 1

⇒ $\frac{5}{6} +\frac{x}{6} = 1$

⇒ $\frac{5+ x}{6} = 1$

⇒ 5 + x = 6

⇒ x = 6/5 = 1.2 hrs

The total time taken by both of them to complete work = 1+1.2 = 2.2hrs

The total taken by both them = 2.2hrs

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