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
:
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
