SOLUTION: It takes 2 hours and 24 minutes for Gail and Bob to paint a room together. If painting alone, it would take Bob 2 hours more to paint the room than it would take Gail. How long d

Question 143802: It takes 2 hours and 24 minutes for Gail and Bob to paint a room together.
If painting alone, it would take Bob 2 hours more to paint the room than
it would take Gail. How long does it take Gail to paint the room?
Please provide the equation necessary to solve.
I know the answer is 4 hours, but I need to show my work. Thanks!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It takes 2 hours and 24 minutes for Gail and Bob to paint a room together.
If painting alone, it would take Bob 2 hours more to paint the room than
it would take Gail. How long does it take Gail to paint the room?
:
Convert 2 hr 24 min to hrs; 2 + 24/60 = 2.4 hrs
:
Let x = time required for G to paint the room alone
:
It says it takes B two hrs longer to do the job, therefore:
(x+2) = B's time to paint it alone
:
Let the completed job = 1
:
Write an equation representing the fraction painted by each person:
;
+ = 1
Multiply equation by x(x+2) to eliminate the denominators:
x(x+2)* + x(x+2)* = x(x+2)(1)
cancel the denominators and you have:
:
2.4x + 2.4(x+2) = x(x+2)
:
2.4x + 2.4x + 4.8 = x^2 + 2x
:
4.8x + 4.8 = x^2 + 2x
:
Arrange as a quadratic equation:
x^2 + 2x - 4.8x - 4.8 = 0
:
x^2 - 2.8x - 4.8 = 0
:
Use the quadratic formula to find the solution:

In this equation: a=1; b=-2.8; c=-4.8

You can do the math, the positive solution should be x = 4

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