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

I just did this! haha

Answer 2

lol its a pain in the butt right

Answer 3

Yes! lol i can help you out though :)

Answer 4

The first thing you're going to do is make a rational equation. Do you know how to do that?

Answer 5

no sorry

Answer 6

Otay, well the equation will be \[\frac{ 1 }{ 8 }+\frac{ 1 }{ 3 }=\frac{ 1 }{ x }\]

Answer 7

ok

Answer 8

Then, itll be \[\frac{ 8+3 }{ 24 }=\frac{ 1 }{ x }\]

Answer 9

if t is the time it takes Jimmy to rake leaves alone, then t - 8 is the time it takes Harry to rake leaves alone.

their rate together is 1/t + 1/(t-8). and given the both did in 3 hours
3[1/t + 1/(t-8)] = 1

t = 12 hours

Answer is 12 hrs

Answer 10

Add 8+3 and cross multiply and divide, itll be 12 like sourwing said

Answer 11

omg thank you guys so much u help me out lot

Answer 12

no problem :)

Answer 13

This problem was closed, but I believe there were some misunderstandings regarding what the problem stated. One time for both working together was not 3 hours, Not the time for Jimmy to complete the job alone. Secondly, Harry can rake leaves 8 times faster than Jimmy, not 8 hours less than Jimmy.

Answer 14

I may have some misunderstanding the problem myself. But I would have solved it this way.
Let X = the time it takes Jimmy to do the job. Then
X/8 = the time it takes Harry to do the job (Harry is 8 times faster than Jimmy)
Together they can accomplish the job in 3 hours.