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?

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) (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
RELATED QUESTIONS
Jenny can cut and split a cord of firewood in 3 fewer hours than Tim can. When they work... (answered by richwmiller)

Jenny can cut and split a cord of firewood in 3 fewer hours than Tim can. When they work (answered by ewatrrr)

Jake can cut and split a cord of firewood in 6 fewer hours than Steve. When they work... (answered by jim_thompson5910)

jake can cut and split a cord of firewood in 6 fewer hours then skyler can. when they... (answered by Fombitz)

Cant figure out this word problem, any help would be nice. Jake can cut and split a... (answered by stanbon)

Joe can cut and split a cord of firewood in 9 fewer hr(s) than Suzie can. When they work (answered by lwsshak3)

Please help solve this problem....thanks. George can cut and split a cord of firewood... (answered by ptaylor)

Kent can cut and split a cord of wood twice as fast as Brent can. When they work... (answered by richwmiller)

Ken can cut and split a cord of wood twice as fast as brent. When they work together, it... (answered by robertb)