SOLUTION: It takes Billy 2 hours to do a certain job than it takes Reena. They worked together for 2 hours; then Reena left, and Billy finished the job in 1 hour. How long would it take each

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Billy 2 hours to do a certain job than it takes Reena. They worked together for 2 hours; then Reena left, and Billy finished the job in 1 hour. How long would it take each      Log On


   

Question 737075: It takes Billy 2 hours to do a certain job than it takes Reena. They worked together for 2 hours; then Reena left, and Billy finished the job in 1 hour. How long would it take each of them to do the job alone?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
It takes Billy 2 hours to do a certain job than it takes Reena. They worked together for 2 hours; then Reena left, and Billy finished the job in 1 hour. How long would it take each of them to do the job alone?
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let x=time it takes Reena to do the job alone
1/x=Her work rate
(x+2)=time it takes Billy to do the job alone
1/(x+2)=His work rate
Work done=time on job*work rate
2%2Fx%2B2%2F%28x%2B2%29%2B1%2F%28x%2B2%29=1
2%2Fx%2B3%2F%28x%2B2%29=1
LCD:x(x+2)
2(x+2)+3x=x(x+2)
2x+4+3x=x^2+2x
x^2-3x-4=0
(x-4)(x+1)=0
x=-1 (reject)
x=4
x+2=6
time it takes Reena to do the job alone=4 hrs
time it takes Billy to do the job alone=6 hrs