SOLUTION: Cant figure out this word problem, any help would be nice. Jake can cut and split a cord of firewood in 6 fewer hours than Mike. When they work together, it takes them 4 hours.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Cant figure out this word problem, any help would be nice. Jake can cut and split a cord of firewood in 6 fewer hours than Mike. When they work together, it takes them 4 hours.      Log On


   

Question 35410: Cant figure out this word problem, any help would be nice.
Jake can cut and split a cord of firewood in 6 fewer hours than Mike. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Jake can cut and split a cord of firewood in 6 fewer hours than Mike. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone?
Let time it takes Mike be "x" hrs.
Then time it takes Jake is "x-6" hrs.
Mike's rate is 1/x job/hr
Jame's rate is 1/(x-6) job/hr
Working together their rate is 1/4 job/hr.
EQUATION:
1/x + 1/(x-6) = 1/4
4(x-6) + 4x = x(x-6)
4x-24 + 4x = x^2-6x
x^2-14+24=0
(x-2)(x-12)=0
x=2 or x=12
Only the x-12 is realistic for this problem.
Mike can do the job in x= 12 hrs.
Jake can do the job in x-6= 6 hrs.
Cheers,
stan H.