Question

A sick programmer was covered at work by two interns. It takes 3 times longer for one of them to do the work than for a programmer, and it takes twice longer for the other intern to do the work than for the same programmer. How many hours would it take a programmer to do all the work if two interns, working together, completed it in 6 hours?

Answer 1

5 hours

Explanation:

Denote the programmer's job rate (job/hour) by R.

The rate for one of the interns is R/3 and for the other R/2.

The two interns work for 6 hours to complete 1 job, so by rate times time equal work done

6(R/3)+6(R/2)=1

2R+3R=1

R=1/5 job/hour

So, it takes the programmer 5 hours