SOLUTION: A boy and a girl work together to type a thesis and it takes them 6 hours. It would take the girl 5 hours more than the boy to type the thesis alone. How long would each need to

Question 42401: A boy and a girl work together to type a thesis and it takes them 6 hours. It would take the girl 5 hours more than the boy to type the thesis alone. How long would each need to type the thesis alone?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Let the time it takes the boy alone to be x. Her time is then x + 5.
The setup for problems like this is
t/A + t/B = 1
where t is the time worked together and A and B are the individual times...so plugging in we get
6/x + 6/(x+5) = 1
now multiply thru by the lowest common denominator, here x(x+5)...and we get
x(x+5)[6/x + 6/(x+5) = 1]
6(x+5) + 6x = x(x+5)
6x + 30 + 6x = x^2 + 5x
now rearrange, factor and solve
x^2 - 7x - 30 = 0
(x - 10)(x + 3) = 0
x = 10 or x = -3
since it cannot be negative time,
x = 10 hours and
x+5 = 15 hours
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