SOLUTION: It takes Bob 4 hours longer to repair a car than it takes Ken. Working together, they can complete the job in 1.5 hours. How long would each of them take working alone.

Question 729664: It takes Bob 4 hours longer to repair a car than it takes Ken. Working together, they can complete the job in 1.5 hours. How long would each of them take working alone.
Found 2 solutions by checkley79, nerdybill:
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
1/4+1/X=1/1.5
1/X=1/1.5-1/4
1/X=(4-1.5)/(1.5*4)
1/X=2.5/6
2.5X=6
X=6/2.5
X=2.4 HOURS FOR KEN WORKING ALONE.
PROOF:
1/4+1/2.4=1/1.5
(2.4+4)/4*2.4=1/1.5
6.4/9.6=1/1.5
9.6*1=6.4*1.5
9.6=9.6
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
It takes Bob 4 hours longer to repair a car than it takes Ken. Working together, they can complete the job in 1.5 hours. How long would each of them take working alone.
.
Let x = time (hours) it takes ken to do job alone
then
x+4 = time it takes bob
.
1.5(1/(x+4) + 1/x) = 1
multiplying both sides by x(x+4):
1.5(x + x+4) = x(x+4)
1.5(2x+4) = x^2+4x
3x+6 = x^2+4x
6 = x^2+x
0 = x^2+x-6
0 = (x+3)(x-2)
x = {-3, 2}
throw out negative solution (extraneous) leaving:
x = 2 hours (Ken)
.
Bob:
x+4 = 2+4 = 6 hours
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