Question

It takes Harland 15 minutes to rake all leaves in the front yard. If Trudy scatters the leaves while Harland rakes, it takes him 20 minutes to rake the leaves. How many minutes does it take Trudy to scatter all the leaves?

Answer 1

If T were to scatters the leaves faster than H rakes them, H would Neve finish raking. So must be over 20 minutes

1/15-1/T=1/20
4/60-1/T=3/60
T=60 mins

So it would take Trudy 60 minutes to scatter all of the leaves

Answer 2

Answer: Trudy takes 60 minutes to scatter all the leaves.

Explanation:

Time taken by Harland to rake all the leaves in the front yard = 15 minutes

Time taken by Trudy scatters the leaves while Harland rakes = 20 minutes

Let time taken by Trudy to scatter all the leaves be x.

Work done by Harland is given by

`(1)/(15)`

Work done by both of them is given by

`(1)/(20)`

According to question,

`(1)/(15)+(1)/(x)=(1)/(20)`

`(1)/(15)-(1)/(20)=(1)/(x)\\\\(4-3)/(60)=(1)/(x)\\\\(1)/(60)=(1)/(x)\\\\x=60\ minutes`

Hence, Trudy takes 60 minutes to scatter all the leaves.