SOLUTION: if chase does a job in 15 hours less time than jacqeline, and they can do the job together in 4 hours, how long will it take each to the job alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: if chase does a job in 15 hours less time than jacqeline, and they can do the job together in 4 hours, how long will it take each to the job alone?      Log On


   

Question 635208: if chase does a job in 15 hours less time than jacqeline, and they can do the job together in 4 hours, how long will it take each to the job alone?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=time it takes Jacqueline to do the job alone
So Jacqueline works at the rate of 1/x of the job per hour
Then x-15 =time it takes Chase to do the job alone
And Chase works at the rate of 1/(x-15) of the job per hour
Together they work at the rate of 1/x + 1/(x-15) of the job per hour
But we are told that they can do the job, working together, in 4 hours
So together they work at the rate of 1/4 of the job per hour
Then our equation to solve is:
1/x + 1/(x-15)=1/4 multiply each term by 4x(x-15)
4(x-15)+4x=x(x-15) simplify
4x-60+4x=x^2-15x collect like terms
x^2-23x+60=0 quadratic in standard form and it can be factored
(x-20)(x-3)=0
x=20 hours---Time it takes Jacqueline to do the job working alone
x-15=20-15=5 hours-----Time it takes Chase to do the job working alone
and
x=3 hours---- IMPOSSIBLE ANSWER---WHY????
CK
1/20+1/5=1/4
1/20+4/20=1/4
5/20=1/4
1/4=1/4
Hope this helps----ptaylor