Question

Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete this job on his own.

Answer 1

t = time it takes Jimmy to rake leaves on his own, then
t - 8 = time it takes Harry to rake leaves on his own

the rate of each person is 1/t and 1/(t-8)

when they work together, the sum of their rate is:
1/t + 1/(t-8)

and it takes them 3 hours, so
[1/t + 1/(t-8)] (3) = 1

solve for t, and t = 12 hours