Biology Forums - Study Force

Working together, Jack and Jill can complete an Electric Circuits assignment in 4 hours. It would take Jack 2 hours longer than Jill to complete the assignment alone. How long would it take Jill alone?

Could someone please show me how to solve this problem algebraically in detail with explanatio? It is a linear systems problem, but I can't seem to figure it out.

Let a=Jack's time and b=Jill's time. However, we are interested in rate, which is inversely proportional to time. Thus, 1/a+1/b=1/4, where 1/a is Jack's rate and 1/b is Jill's rate, where the units of rate are inverse hours.

We need to express a in terms of b or b in terms of a. According to the problem, Jill works two hours faster than Jack, so a=b+2 or b=a-2

From there, we can solve the system by substitution.

This problem appears to produce two non integer solutions, one of which is erroneous.

I know the solution to this problem, but I never knew why it was 1 over a, and 1 over b, and 1 over 4. That's what was throwing me off, confusing me big time.

Thanks for the response.