Question

It takes Jack 3 hours to fence one side of a fence. It takes Adam 5 hours. How long would it take them if they worked together?

Answer 1

Hint: We are given the time they take to complete the paint of one side of the fence. We will first determine the work done by Jack and Adam in one hour separately. Then we will find the amount of work they will complete in one hour. Then we will find the time they together take to complete the whole work.

Complete step by step solution:
We are given that Jack takes 3 hours to fence one side of a fence whereas Adam takes 5 hours to do the same thing.
It clearly states that in one hour Jack completes \[\dfrac{1}{3}\] amount of work and Adam completes \[\dfrac{1}{5}\] amount of work.
Now in one hour they together can complete \[\dfrac{1}{3} + \dfrac{1}{5}\] amount of work.
That is taking LCM
 \[\dfrac{1}{3} + \dfrac{1}{5} = \dfrac{{5 + 3}}{{3 \times 5}}\]
\[ = \dfrac{8}{{15}}\]
This is the amount of work done by them in one hour equals to \[\dfrac{1}{{\dfrac{8}{{15}}}}\]
This is nothing but to complete the work we will multiply the ratio with \[\dfrac{{15}}{8}\] and this is the time taken by both of them to complete the work.
This is nothing but \[1\dfrac{7}{8}\] that is 1 full hour and \[1.875\] minutes.

So the answer can be \[\dfrac{{15}}{8}\] hours or \[1\dfrac{7}{8}\] hours or \[1.875\] hours.

Note: Note that we are given the time taken by them to complete the work. from that we have found the amount of work they complete in one hour.
If x is the work done by A in one hour and y is the work done by B in one hour so they together can complete \[\dfrac{{x + y}}{{xy}}\] this much amount of work. We can directly use this formula to find the work done by them in one hour. Now observe that work completes means the status should be 1. So we multiplied the ratio with the number that makes the ratio 1. And that was the time taken by them to complete the work.