Question

Henry can paint a small house in 3 days, Ruby can paint a small house in 4 days, and Charlie can paint a small house in 5 days. How long will it take for Henry, Ruby and Charlie to paint one small house together? Give your answer as a fraction.

Answer 1

So it will take them 1 day 6 hours and 39 minutes to paint one small house.

Explanation:

Henry can paint 1 small house in 3 days so he can paint 1/3 or .3333 in a day

Ruby can paint 1 small house in 4 days so she can paint 1/4 or .25 in a day

Charlie can paint 1 small house in 5 days so he can paint 1/5 or .2 in a day

Together, that means they pain .3333 + .25 + .2 of a house per day. That's an daily rate of:

.3333 + .25 + .2 = .78333

The portion of the house they clean in x days is .78333x. We'd like to know how long it will take them to paint 100% or 1 of the house. So:

.78333x = 1 Divide each side by .78333

x = 1/.78333

x ≈ 1.277

Let's convert .277 to hours by multiplying by 24

.277 * 24 = 6.65

Let's convert .65 to minutes by multiplying by 60

.65 * 60 = 39

So it will take them 1 day 6 hours and 39 minutes to paint one small house.

Answer 2

1.277 days

Explanation:

H paint .3333 a day R paint .25 a day Charlie paint .2 a day

.3333 + .25 + .2 = .78333

x is number of days to paint.

.78333x = 1

x = 1/.78333 = 1.277

1.277 days