SOLUTION: john can cut and split a cord of firewood in 6 fewer hours than tim can. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: john can cut and split a cord of firewood in 6 fewer hours than tim can. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone?      Log On


   

Question 354179: john can cut and split a cord of firewood in 6 fewer hours than tim can. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
let j=time John works to complete the job
let t=time Tim works to complete the job
--
give
j=t-6
each our working together they complete 1/j+1/t=1/(t-6) + 1/t of the job
together it takes 4 hours to complete the job
therefore 4*(1/(t-6)+1/t)=1
--
multiply by GCD t*(t-6) both side
4*(t+t-6))=t*(t-6)
4*(2t-6)=t^2-6t
8t-24=t^2-6t
0=t^2-14t+24
0=(t-2)*(t-12)
--
t=2 or t=12
if t=2 then t-6=-4 not a solution since time has to be positive for both
t=12 then t-6=6
so Tim takes 12 hours and John takes t-6 or 6 hours working alone