SOLUTION: 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

Question 52821This question is from textbook
: 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? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
:
Let t = time required for Tom to complete it.
:
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

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