Question

An experienced roofer can roof a house in 26 hours. A beginning roofer needs 39 hours to complete the same job. Find how long it takes for the two to do the job together

Answer 1

the answer is 13 hours because 39-26=13.

Answer 2

The way to do this is to use the formula
1/r1 + 1/r2 = 1/rt
r1 = time for roofer 1 in hours = 26 hours.
r2 = time for roofer 2 in hours = 39 hours.

1/26 + 1/39 = 1/rt
0.03846 + 0.02564 = 1/rt
0.06410 = 1/rt ****** (I've used these stars later on. Ignore them now)

You could go on one of two ways. You could put 1 one under 0.06410 and cross multiply. I'll do that first.

0.06410 / 1 = 1/rt
0.06410 * rt = 1 * 1
0.06410 * rt = 1 Now divide by the number on the left.
rt = 1/0.06410
rt = 15.6

Or you could do this. Go back to the step with the stars.
Turn both steps upside down

0.06410 = 1 / r2 Take the reciprocal of both sides.
1/0.06410 = r2
r2 = 15.6 hours for both roofers working together.

There are other ways of doing this problem. None are any quicker. The point is that your answer should come to a number below either of the workers. It makes sense. The slower worker still does some work, but the faster worker does most of it.