SOLUTION: It takes James 2 hours longer to do a certain job than it take Philip. They worked together for 3 hours; then Philip left and James finished the job for 1 hour. How long would it t
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-> SOLUTION: It takes James 2 hours longer to do a certain job than it take Philip. They worked together for 3 hours; then Philip left and James finished the job for 1 hour. How long would it t
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Question 819307: It takes James 2 hours longer to do a certain job than it take Philip. They worked together for 3 hours; then Philip left and James finished the job for 1 hour. How long would it take each of them to do the job alone? Found 2 solutions by ankor@dixie-net.com, richwmiller:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! It takes James 2 hours longer to do a certain job than it take Philip.
They worked together for 3 hours; then Philip left and James finished the job for 1 hour.
How long would it take each of them to do the job alone?
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Let t = time required by Philip to do the job
then
(t+2) = time required by James
:
Let the completed job = 1
:
IN the shared work equation J works 4 hrs and P works 3 hrs + = 1
multiply by t(t+2), cancel the denominators and you have:
4t + 3(t+2) = t(t+2)
4t + 3t + 6 = t^2 + 2t
7t + 6 = t^2 + 2t
Combine to form a quadratic equation the right
0 = t^2 + 2t - 7t - 6
t^2 - 5t - 6 = 0
Factors to
(t-6)(t+1) = 0
The positive solution is all we want here
t = 6 hrs for Philip alone
then, obviously:
6 + 2 = 8 hrs for James alone
:
:
You can check this in the shared work equation + = 1
You can put this solution on YOUR website! It takes James 2 hours longer to do a certain job than it take Philip. They worked together for 3 hours; then Philip left and James finished the job for 1 hour. How long would it take each of them to do the job alone?
j=p+2,
3/j+3/p+1/j=1
4/j+3/p=1
4/(p+2)+3/p=1
j = 8, p = 6
