Question

. Patrick, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same hob together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms?

Answer 1

Answer: 15 hours

Explanation:

Given : Patrick, by himself, can paint four rooms in 10 hours.

i..e Time taken by Patrick to paint the 4 walls = 10 hours.

Since rate of work =
`(Work)/(Time)`

We consider the entire job as 1.

Then, the rate of work done by Patrick =
`(1)/(10)`

If he hires April to help, they can do the same hob together in 6 hours.

i.e. the rate of work done by Patrick and April together =
`(1)/(6)`

Then, the rate of work done by April = rate of work done by Patrick and April together - rate of work done by Patrick

`(1)/(t)=(1)/(6)-(1)/(10)\\\\\Rightarrow\ (1)/(t)=(10-6)/(60)=(4)/(60)\\\\\Rightarrow\ (1)/(t)=(1)/(15)\\\\\Rightarrow\ t=15`

Hence,it will take 15 hours April to paint four rooms .