Question

Please Help!!
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

Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. 
If they join to work together they can complete the job in 3 hours. 
1/x + 1/(x - 8) = 1/3 
3(x - 8) + 3x = x(x - 8) 
x^2 - 14x + 24 = 0 
(x - 12)(x - 2) = 0 
Solutions: 
x = 2 
x = 12 
Jimmy can complete the job on his own in 12 hours.