Question

It takes three men six hours to repair a road . How long would it have taken two men?​

Answer 1

9 hours

Explanation:

The time taken is inversely proportional to the number of men; if M = number of men and D = number of days this can be expressed as

`D \displaystyle \propto } (1)/(M)\\\\\text{which can be expressed as an equation: }\\\\D = k \cdot (1)/(M)\\\\or\\\\D = (k)/(M)\\\\`

k is known as the constant of proportionality which can be expressed as

`k = D\cdot M`

Inversely proportional means:
As the number of men increases, the time taken decreases

As the number of men decreases, the time taken increases

We can find k from the given information with M = 3 and D = 6 hours

`k = 6 \cdot 3 = 18`

`\textrm{Therefore, given M= 2, D = $(18)/(2) = 9$ \;hours}`

For 2 men it will take 9 hours to repair the road