Answer :
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 [tex]\frac{1}{t}[/tex].
We have been given that Brad paints a house in 5 days, so part of house painted by Brad in 1 day would be [tex]\frac{1}{5}[/tex].
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 [tex]\frac{1}{3}[/tex].
Now, we will equate sum of work done by both brothers with [tex]\frac{1}{3}[/tex] to solve for t as:
[tex]\frac{1}{t}+\frac{1}{5}=\frac{1}{3}[/tex]
[tex]\frac{1}{t}\times 15t+\frac{1}{5}\times 15t=\frac{1}{3}\times 15t[/tex]
[tex]15+3t=5t[/tex]
[tex]15+3t-3t=5t-3t[/tex]
[tex]15=2t[/tex]
[tex]2t=15[/tex]
[tex]\frac{2t}{2}=\frac{15}{2}[/tex]
[tex]t=7.5[/tex]
Therefore, it will take 7.5 days for the Nick to paint the house alone.