SOLUTION: Aira can do a job in 4 hours and Queenie can do the same in 9 hours. They start working together. After 2 hours, Queenie leaves and Aira finishes the job alone. How many hours did

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Aira can do a job in 4 hours and Queenie can do the same in 9 hours. They start working together. After 2 hours, Queenie leaves and Aira finishes the job alone. How many hours did       Log On


   

Question 982505: Aira can do a job in 4 hours and Queenie can do the same in 9 hours. They start working together. After 2 hours, Queenie leaves and Aira finishes the job alone. How many hours did Aira take to finish the job alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the fraction of the job they
do working together for 2 hrs
Aira's rate of working is:
[ 1 job done / 4 hrs ]
Queenie's rate of working is:
[ 1 job done / 9 hrs ]
----------------------------
Add their rates of working to get
their rate working together
Their rate working together is: +x%2F2+
+1%2F4+%2B+1%2F9+=+x%2F2+
Multiply both sides by +36+
+9+%2B+4+=+18x+
+18x+=+13+
+x+=+13%2F18+
In 2 hrs, they do +13%2F18+ of the work. That
means there is +1+-+13%2F81+=+5%2F18+
of the work left to do
-------------------------
Let +t+ = time in hrs for Aira to
finish the job
+1%2F4+=+%28%28+5%2F18+%29%29+%2F+t+
+1%2F4+=+5%2F%2818t%29+
Multiply both sides by +36t+
+9t+=+10+
+t+=+10%2F9+=+1+%2B+1%2F9+
+%28+1%2F9+%29%2A60+=+6+%2B+2%2F3+
+%28+2%2F3%29%2A60+=+40+
---------------------
Aira finishes the job in 1 hr 6 min 40 sec
check answer:
+1%2F4+=+%28%28+5%2F18+%29%29+%2F+t+
+1%2F4+=+%28%28+5%2F18+%29%29+%2F+%28%28+10%2F9+%29%29+
+1%2F4+=+%28+5%2F18+%29%2A%28+9%2F10+%29+
+1%2F4+=+%28+5%2F10+%29%2A%28+9%2F18+%29+
+1%2F4+=+%28+1%2F2+%29%2A%28+1%2F2+%29+
+1%2F4+=+1%2F4+
OK
Hope I got it!