SOLUTION: For a certain amount of work, David takes six hours less than Jody. If they work together it takes them thirteen hours twenty minutes. How long will it take david alone to complete

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Question 1025595: For a certain amount of work, David takes six hours less than Jody. If they work together it takes them thirteen hours twenty minutes. How long will it take david alone to complete the work
Answer by ikleyn(52794) About Me  (Show Source):
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For a certain amount of work, David takes six hours less than Jody. If they work together it takes them
thirteen hours twenty minutes. How long will it take David alone to complete the work
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Let D = time needed for David to complete the job, in hours, and
let J = time needed for Jodi  to complete the job.

According to the condition, 

D = J - 6.     (1)

David's rate-of-work is 1%2FD; Jodi''s rate-of-work is 1%2FJ.

Their combined rate-of-work is 1%2FD+%2B+1%2FJ.

According to the condition, 

1%2FD+%2B+1%2FJ = 1%2F%28%2840%2F3%29%29.   (2)     ( <--- 40%2F3 = 131%2F3)

Now substitute (1) into (2) and simplify the right side in (2). You will get

1%2F%28J-6%29+%2B+1%2FJ = 3%2F40.    (3)

To solve (3), multiply both sides by 40*J*(j-6). You will get

40J + 40*(J-6) = 3*J*(J-6).

Simplify and solve it:

80J+-+240 = 3%2AJ%5E2+-+18J,

3%2AJ%5E2+-+98J+%2B+240 = 0.

Apply the quadratic formula to get the roots.

They are 30 and 22%2F3.

Notice that the solution for Jody must be greater than 6 hours, in order J-6 was meaningful. 

It gives the only solution of 30 hours for Jody and D = J-6 = 24 hours for David.