# It takes mary 3 hours more to do a job than its takes jane.If they work together, they can finish the same job in two hours.How long would its takes mary to finish the job alone?

2
by dhiannechelle

2015-06-06T21:08:39+08:00

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We let the time that Jane takes to finish the job be x, so for Mary it is x+3.
This makes the rates of Jane and Mary be 1/x and 1/(x+3) respectively.
1/[1/x + 1/(x+3)] = 2
1 = 2/x + 2/(x+3)
1 = (4x+6)/(x²+3x)
x²+3x = 4x+6
x²-x-6 = 0

Method 1: Guess and Check
We look for two number with a product of 6 and an absolute difference of 1
6 - 1 = 5  X
3 - 2 = 1  √
So: (x-3)(x+2)=0
Therefore x is either 3 or -2 but we cannot have a negative time so we only consider 3. Therefore Mary's time is 6 hours. It takes her 6 hours to do it alone.

Method 2: Quadratic Formula
x = 1 ± √(1+24) = ± 5 = -2 or 3
2             2
Again, we cannot have a negative value. So Jane's time is 3 hours and Mary's is 6 hours. So the answer is 6 hours.
2015-06-07T06:07:24+08:00
It will takes Mary to finish the job alone in 6 hours