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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?

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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)__ = __1 ____± 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.

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 =

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.