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

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.

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