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Please help me ASAP!!! I HAVE NO IDEA HOW TO DO THIS!!!!

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.

4 answers

John's rate = 1/12
Rick's rate = 1/15
Molly's rate = 1/x

cominged rate = 1/12 + 1/15 + 1/x
= (5x + 4x + 60)/60x

so 1 / ( (5x + 4x + 60)/60x ) = 6
60x/(9x + 60) = 6
54x + 360 = 60x
x = 60
Molly's cand do the room in 60 hours by herself

check: 1/12 + 1/15 + 1/60 = 1/6 , as needed
THANK YOU SO MUCH!!!!!
a. 1/T1 + 1/T2 + 1/T3 = 1/6,
1/12 + 1/15 + 1/T3 = 1/6.

b. LCD = 60.

c. 1/12 + 1/15 + 1/T3 = 1/6,
1/T3 = 1/6 - 1/12 - 1/15,
1/T3 = 10/60 - 5/60 - 4/60 = 1/60,
T3 = 60 hrs. = Molli's time.
Thank you!:-)
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