Question 52821
 It takes Terry 2 hours longer to do a certain job than it takes Tom. They worked together for 3 hours. Then Tom left and Terry finished the job in one hour. How long would it take each of them to do the job alone?
:
Let the completed job = 1
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Let t = time required for Tom to complete it.
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Then [t+2] = Terry's time to do it.
:
Working together, Tom worked 3 hrs and Terry worked 4 hrs.
:
       Tom  +  Terry   = 1
       3/t  +  4/(t+2) = 1
:
Mult eq by t(t+2) and you have:
       3(t+2) + 4t = 1[t(t+2)]
:
       3t + 6 + 4t = t^2 + 2t
:
                0  =  t^2 + 2t - 3t - 4t - 6
:
                0  = t^2 - 5t - 6
:
                0  = [t-6][t+1]
:
                t  = +6
                t  = -1
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The positive solution is 6 hrs for Tom to do the job by himself
Then Terry would take 8 hrs to do it.
:
Check by substitution:  3/6  +  4/8  = 1