SOLUTION: It takes Tom 3 hours less to paint a fence than Jim. If the two boys work together, they can paint the fence in 2 hours. How many hours would each boy, working alone, need to paint

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Question 128173: It takes Tom 3 hours less to paint a fence than Jim. If the two boys work together, they can paint the fence in 2 hours. How many hours would each boy, working alone, need to paint the fence?
Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!
1. Set up the variables:
Let x = # hours it takes Jim to paint the fence alone
Let x - 3 = # hours it takes Tom to paint the fence alone
Let 1/x = amount of the fence painted by Jim in 1 hour
Let 1%2F%28x+-+3%29 = amount of the fence painted by Tom in 1 hour
2. Set up the equation(s)
In 1 hour the two boys paint
1%2Fx+%2B+1%2F%28x-3%29 of the fence
In 2 hours the two boys paint:
2=+1 (1 = 1 job or 100% of the job)
2%2Fx+%2B+2%2F%28x-3%29=+1
3. Find the common denominator: (x)(x-3)= x%5E2+-+3x

4. Multiply both sides of the equation by (x^2 - 3x):
2%28x-3%29+%2B+2x+=+x%5E2+-+3x
5. Combine like terms:
2x+-+6++%2B+2x+=+x%5E2+-+3x
4x+-+6+=+x%5E2+-+3x
0+=+x%5E2+-+7x+%2B+6
6. Factor and solve for x:
%28x+-+1%29%28x+-+6%29+=+0
x+=+1 or x+=+6
Since we have two answers we need to see which one makes sense by plugging each into our equations:
Jim can paint a fence in x = 1 hours
Tom can paint a fence in x-3 = -2 hours
We must reject this answer because time can never be a negative value.
Substitute x = 6:
Jim can paint the fence in x+=+6 hours
Tom can paint the fence in x+-+3+=+6+-+3+=+3 hours
This is the answer we are looking for.