Question

John, Rick, and Molli can paint a room working together in 6 hours. Alone, John can paint the room in

12 hours. If Rick works alone, he can paint the room in 15 hours. Write an equation comparing the
group rate to the sum of the individual rates. Then find how long it will take Molli to paint the room if
working alone.

a. What is the equation?

b. What is the lowest common denominator for the equation in part a?

c. Show all work below in solving equation from part a.

Answer 1

a.
`(1)/(m)(6)+(1)/(12) (6)+(1)/(15) (6) =1`

b. 60hrs

Explanation:

Let the time Molli will take to pint the room to be = t

Thus the amount of room that Molli can paint in 1 hour= 1/m

The amount of room John can paint is 1 hour= 1/12

The amount of room Rick can paint in 1 hour = 1/15

The equation for working together at a rate x time per work done will be;

`(1)/(m) *6+(1)/(12) *6+(1)/(15) *6=1`

You multiply by 6 in the three terms of the equation because it takes 6 hours for John, Rick and Molli to complete painting.

`(6)/(m) +(1)/(2) +(2)/(5) =1`

multiply by 10m in every part of the expression because 10m is the Least Common Multiple(LCM) is this case

Collect like terms and find value of m

`60+5m+4m=10m\\\\60+9m=10m\\\\60=10m-9m\\\\60=m`

Molli will take 60 hours to paint the room if working alone