Jack can paint a house in 5 days, and Richard can paint the same house in 7 days. Working together, how long will it take them to finish the job?

In order to simplify the problem, I will solve it without using fractions.

First,  we should find the least common multiple(LCM) of the days needed for Jack and Richard to paint a house. Normally, we would use a specific method to find the LCM but in this problem, we know that 7 and 5 are coprime( here a question might appear) numbers and, therefore, we can find it by multiplying the numbers => 7*5=35.

Now, we can say that Jack can paint 35 days/ 5 days = 7 houses. For the same time, Richard could paint 35 days/ 7days = 5 houses. Thus, if they worked together, they would paint 5+7=12 houses for 35 days.

We are asked to find how many days do Jack and Richard need to paint only one house. The answer would be 35 days/ 12 houses = 2 and 11/12 days