Question

"joins" "together" Brad paints a house in 5 days. When his brother Nick joins him, they can paint a house in 3 days. How long does it take Nick to paint the house alone

Answer 1

Answer:

7.5 days.

Step-by-step explanation:

Let t represent time taken by Nick in days to paint the house alone.

Part of house painted by Nick in 1 day would be $\frac{1}{t}$.

We have been given that Brad paints a house in 5 days, so part of house painted by Brad in 1 day would be $\frac{1}{5}$.

We are also told that when Brad's brother Nick joins him, they can paint a house in 3 days. So part of house painted by both Brad and Nick together in 1 day would be $\frac{1}{3}$.

Now, we will equate sum of work done by both brothers with $\frac{1}{3}$ to solve for t as:

$\frac{1}{t}+\frac{1}{5}=\frac{1}{3}$

$\frac{1}{t}\times 15t+\frac{1}{5}\times 15t=\frac{1}{3}\times 15t$

$15+3t=5t$

$15+3t-3t=5t-3t$

$15=2t$

$2t=15$

$\frac{2t}{2}=\frac{15}{2}$

$t=7.5$

Therefore, it will take 7.5 days for the Nick to paint the house alone.