SOLUTION: Abel and ben working together can accomplish a task in 6 hrs 40 mins. after working with Ben for 3 hrs. Abel beacame ill and Ben was left alone to finish the job which he did in 8

Question 757238: Abel and ben working together can accomplish a task in 6 hrs 40 mins. after working with Ben for 3 hrs. Abel beacame ill and Ben was left alone to finish the job which he did in 8 hrs. and 15 mins. How long would it take each working alone to do the job?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Abel and ben working together can accomplish a task in 6 hrs 40 mins. after working with Ben for 3 hrs. Abel became ill and Ben was left alone to finish the job which he did in 8 hrs. and 15 mins. How long would it take each working alone to do the job?
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Abel's rate is "a" ; Ben's rate is "b".
Together DATA: time = 6 2/3 hrs = 20/3 hrs ; a+b = 3/20 job/hr
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Equation:
3 hrs together + (33/4)hr for Ben = 1 job done
3(a+b) + (33/4)b = 1
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3(3/20) + (33/4)b = 1
Multiply thru by 20 to get:
9 + 165b = 20
165b = 11
b = 1/15 job/hr (Ben's rate)
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Time for Ben to do the job alone: 15 hrs/job
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Solve for "a":
a + b = 3/20
a + 1/15 = 3/20
a = 3/20 - 1/15 = (45-20)/300 = 25/300 = 1/12 job/hr
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Abel's time to do the job alone = 12 hr/job
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Cheers,
Stan H.
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