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

It takes Nick alone 7.5 days to finish painting a house.

Step-by-step 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