Question

Bob can do a job in 5 hours while Bill can do the same job in 8. How many hours would it take them, working together, to do this job?

Answer 1

Since we are basing this problem on hours, we have to look at how much of the job gets done by each person in 1 hour. If it takes Bob 5 hours to do the whole job, he can get 1/5 of it done in an hour; likewise, if it takes Bill 8 hours to do the whole job, he can get 1/8 of the job done in an hour. We are combining their efforts by addition and setting it equal to 1/x, x being the number of hours it takes them to do the job together. Since the number of hours is in the denominator for Bob and Bill, the number of hours has to also be in the denominator for the solution. $\frac{1}{5}+\frac{1}{8}=\frac{1}{x}$. Of course in order to add those we need a common denominator, which happens to be 40. Therefore, $\frac{8}{40}+\frac{5}{40}=\frac{1}{x}$, and $\frac{13}{40}=\frac{1}{x}$. Cross multiply to get 13x = 40. Divide by 13 to find that it takes them just over 3 hours to get the job done together. 3.07 hours to be exact.