SOLUTION: Jerry works 3 hours faster than David. Together they complete 5 jobs in 18 hours. How long does it take Jerry alone? jerry = x dave = x+3 1/x * 18 + (1/x+3) * 18 = 5 I th

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Question 587628: Jerry works 3 hours faster than David. Together they complete 5 jobs in 18 hours. How long does it take Jerry alone?
jerry = x
dave = x+3
1/x * 18 + (1/x+3) * 18 = 5
I think....but it just doesn't work how I think it should. I appreciate your help.
Found 3 solutions by nerdybill, lwsshak3, Alan3354:
Answer by nerdybill(7384)   (Show Source):
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Yes, you have it right.
1/x * 18 + (1/x+3) * 18 = 5
18/x + 18/(x+3) = 5
multiplying both sides by (x)(x+3):
18(x+3) + 18x = 5(x)(x+3)
18x+54 + 18x = 5(x^2+3x)
36x+54 = 5x^2+15x
54 = 5x^2-21x
0 = 5x^2-21x-54
0 = 5x^2-30x+9x-54
0 = (5x^2-30x) + (9x-54)
0 = 5x(x-6) + 9(x-6)
0 = (x-6)(5x+9)
x = {-9/5, 6}
throw out the negative solution (extraneous) leaving:
x = 6 hours

Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website!
Jerry works 3 hours faster than David. Together they complete 5 jobs in 18 hours. How long does it take Jerry alone?
**
First, I will assume the work rates for David and Jerry are for one job.
let x=hours for Jerry to complete one job alone
5x=hours for Jerry to complete 5 jobs alone
1/5x=work rate for Jerry to complete 5 jobs
..
(x+3) hours for David to complete one job alone
5(x+3) hours for David to complete 5 jobs alone
1/5(x+3)=work rate for David
..
It took18 hours to complete 5 jobs (100%)
18/5x+18/5(x+3)=1
LCD:5x*5(x+3)
18*5(x+3)+18*5x=5x*5(x+3)
90x+270+90x=25x^2+75x
25x^2-105x-270=0
divide by 5
5x^2-21x-54=0
(5x+9)(x-6)=0
5x+9=0
x=-9/5 (reject, x>0)
x-6=0
x=6
Ans:
hours for Jerry to complete one job alone=6 hrs
hours for Jerry to complete 5 jobs alone=5x=30 hrs
..
Note:your set up correctly found the hours for Jerry to complete one job alone, but I see the problem better the way I set it up.

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
Jerry works 3 hours faster than David.
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That makes no sense.
Do you mean it takes Jerry 3 hours less to do the work?
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If so, you should say that.