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?
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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/x+2/(x+2)+1/(x+2)=1}}}
{{{2/x+3/(x+2)=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