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.

Click here to see ALL problems on Rate-of-work-word-problems

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