Question

It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate? 

Answer 1

$\textbf{SOLUTION:}$

$<b>The number of men is inversely proportional to the time taken to do the job.$

Let t be the time taken for the 8 men to finish the job.

4 × 6 = 8 × t

24 = 8t

t = 3 hours

Answer 2

Given:

It takes 4 men 6 hours to repair a road.

To Find:

How long will it take 8 men to do the job if they work at the same rate?

Solution:

It is given that 4 men take 6 hours to do a job and we need to find how much time will it take to do the same job by 8 men

Either we can solve it proportionally like the amount of work is same in both cases but the amount of men has doubled so to maintain the proportionality the amount of time will need to be half of what it used to be so it will be 6/2=3 hours.

Or we can solve it by a formula which is very useful in these types of questions

$\frac{M_{1}D_{1}H_{1}}{W_{1}} =\frac{M_{2}D_{2}H_{2}}{W_{2}}$

where,

          M= No of men

          D= No of days

          H= No of hours

          W= Amount of work

So now putting the values according to the question we get

$4*6=8*x\\x=3$

Hence, it will take 8 men to do the same job in 3 hours.