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

Step-by-step 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 = $\dfrac{Work}{Time}$

We consider the entire job as 1.

Then, the rate of work done by Patrick = $\dfrac{1}{10}$

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 = $\dfrac{1}{6}$

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

$\dfrac{1}{t}=\dfrac{1}{6}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{10-6}{60}=\dfrac{4}{60}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{15}\\\\\Rightarrow\ t=15$

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