Question

16.) a) A group of college students are volunteering for Help the Homeless during their

spring break. They are putting the finishing touches on a house they built. Working
alone, Irina can paint a certain room in 5 hours. Paul can paint the same room in 10
hours. How many hours will it take them to paint the room?
bl Raul

Answer 1

`3(1)/(3)` or
`(10)/(3)`

Explanation:

We could use the combined rate equation to find the combined rate of work.

Combined rate of work formula:
`(1)/(t_(b)) = (1)/(t_(1) ) + (1)/(t_(2) )`, where
`t_(1)` is the individual time for object A,
`t_(2)` the individual time for object B and
`t_(b)` is the time for A and B together.

The time it takes Irina to paint the room alone,
`t_(1)` = 5 hours

The time it takes Paulo to paint the room,
`t_(2)` = 10 hours

1) Substitute object A (Irina) and B (Paulo) into the formula given above, and change
`t_(b)` into an
`x`.

`\frac{1}{{x}} = (1)/(5 ) + (1)/(10 )`

2) Add the fractions.

`(1)/(x) = (3)/(10)`

3) Solve for the
`x`.

`x(3) = 1(10)\\3x = 10\\x = (10)/(3) \\`

4) Change them into a mixed fraction.

`3(1)/(3)`

Note:
`(10)/(3)` or
`3(1)/(3)` are both correct. Write the answer according to the question. In this case, there is no specific rule, so I choose
`3(1)/(3)`.