Answer:
It takes Nick alone 7.5 days to finish painting a house.
Explanation:
Let the speed of Brad's painting be B
Let the speed of Nick's painting be N
And let the amount of work required to paint a house be H
Let the time it takes Nick alone to finish painting a house be t
(Speed of painting) = (amount of work to be done)/(total time it takes to finish)
From the question,
B = (H/5) (eqn 1)
N = (H/t) (eqn 2)
But they both paint a house in 3 days
In 3 days, Brad does (3×B) amount of work and Nick does (3×N) amount of work too.
Therefore, H = 3B + 3N (eqn 3)
Recall (eqn 1) and (eqn 2) and substitute for B and N in (eqn 3)
H = 3B + 3N
B = (H/5); N = (H/t)
H = (3H/5) + (3H/t)
1 = (3/5) + (3/t)
Multiply through by 5t
5t = 3t + 15
5t - 3t = 15
2t = 15
t = (15/2) = 7.5 days