Sara can wash a boat in 10 hours. If Benny helps, it takes them 8 hours. Without help, how long would it take Benny to finish this job ?

Answer 1

Their combined work-rate is 1/8; that is , they wash 1/8 of the boat per hour

Sara's work-rate is 1/10; that is, she can wash 1/10 of the boat per hour

So 1/10 + B = 1/8 , where b is Ben's work-rate

B = 1/8 - 1/10 = (10-8)/80 = 2/80 = 1/40

It will take him 40 hours to wash the boat

Answer 2

(1/10) + 1/B = 1/8

Solve it: B = 40

This seems unreasonably long, but I believe it is correct.

Now why the reciprocal? These are rates!