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?

5 hours

Step-by-step 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

The answer is "Square the number of the term, n"

Notice the pattern
1^2 = 1*1 = 1
2^2 = 2*2 = 4
3^2 = 3*3 = 9
4^2 = 4*4 = 16
5^2 = 5*5 = 25
6^2 = 6*6 = 36
the pattern goes on forever

In general, if n is any number then we have n^2 = n*n as the term
Ie, nth term is n^2

In our case, the next term is the 6th term with n = 6, so n^2 = 36