SOLUTION: jake can cut and split a cord of firewood in 6 fewer hours then skyler 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: jake can cut and split a cord of firewood in 6 fewer hours then skyler 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 324046: jake can cut and split a cord of firewood in 6 fewer hours then skyler 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 Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Output
Rj%28T-6%29=1
Rj=1%2F%28T-6%29
Rs%28T%29=1
Rs=1%2FT
.
.
.
%28Rj%2BRs%294=1
Rj%2BRs=1%2F4
1%2F%28T-6%29%2B1%2FT=1%2F4
4T%2F%28T%28T-6%29%29%2B%284%28T-6%29%29%2F%28T%28T-6%29%29=T%28T-6%29%2F%28T%28T-6%29%29
4T%2B4T-24=T%5E2-6T
T%5E2-14T-24=0
Use the quadratic formula,
T+=+%2814+%2B-+sqrt%2814%5E2-4%2A1%2A%28-24%29+%29%29%2F%282%2A1%29+
T+=+%2814+%2B-+sqrt%28196%2B96+%29%29%2F2+
T+=+%2814+%2B-+sqrt%28292%29%29%2F2+
T+=+%2814+%2B-+2sqrt%2873%29%29%2F2+
T+=+7+%2B-+sqrt%2873%29+
Only the positive value makes sense for our problem.
It takes Skyler T hrs or 7%2Bsqrt%2873%29 hrs.
It takes Jake T-6 hrs or 1%2Bsqrt%2873%29 hrs.