Question

Write an equation that can be used to solve the problem. Then answer the question asked. A group of college students are volunteering for Habitat for Humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Dale Horton can paint a certain room in 3 hours. Kathy Garcia can paint the same room in 9 hours. How long will it take them working together to paint the room?

Answer 1

Required equation :
`(1)/(t)=(1)/(3)+(1)/(9)`

Together they can paint the same room in 2.25 hours or 2 hours 15 minutes.

Explanation:

It is given that Dale Horton can paint a certain room in 3 hours.

One hour woks of Dale Horton = 1/3

Kathy Garcia can paint the same room in 9 hours.

One hour woks of Kathy Garcia = 1/9

Let together they can paint the same room in t hours.

One hour woks of both = 1/t

`(1)/(t)=(1)/(3)+(1)/(9)`

`(1)/(t)=(3+1)/(9)`

`(1)/(t)=(4)/(9)`

After reciprocal we get

`(t)/(1)=(9)/(4)`

`t=2.25`

1 hour = 60 minutes.

0.25 hour = 15 minutes.

Therefore, together they can paint the same room in 2.25 hours or 2 hours 15 minutes.