SOLUTION: One computer takes 21 minutes longer than a second computer to do the job. Working together these computers can do the same job in 10 minutes. How long would it take each computer

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One computer takes 21 minutes longer than a second computer to do the job. Working together these computers can do the same job in 10 minutes. How long would it take each computer       Log On


   

Question 528667: One computer takes 21 minutes longer than a second computer to do the job. Working together these computers can do the same job in 10 minutes. How long would it take each computer working alone to do the same job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rate of doing jobs to get
their rate together.
Let t = the time in minutes for the 2nd computer
to finish the job.
Then +t+%2B+21+ is the time for the 1st computer
to do the job
+1%2F%28+t+%2B+21%29+ is the 1st computer's rate
+1%2Ft+ is the 2nd computer's rate
+1%2F10+ is their rate working together
+1%2F%28t+%2B+21%29+%2B+1%2Ft+=+1%2F10+
Multiply both sides by +t%2A%28t+%2B+21%29%2A10+
+10t+%2B+10%2A%28t+%2B+21%29+=+t%2A%28t+%2B+21%29+
+10t+%2B+10t+%2B+210+=+t%5E2+%2B+21t+
+t%5E2+%2B+t+=+210+
Complete the square
+t%5E2+%2B+t+%2B+%281%2F2%29%5E2+=+210+%2B+%28t%2F2%29%5E2+
+%28+t+%2B+1%2F2+%29%5E2+=+840%2F4+%2B+1%2F4+
+%28+t+%2B+1%2F2%29%5E2+=+841%2F4+
+%28+t+%2B+1%2F2%29%5E2+=+%2829%2F2%29%5E2+
+t+%2B+1%2F2+=+29%2F2+
+t+=+28%2F2+
+t+=+14+ ( ignore the negative square root )
+t+%2B+21+=+35+
It will take the 1st computer 35 min
It will take the 2nd computer 14 min
check:
+1%2F%28t+%2B+21%29+%2B+1%2Ft+=+1%2F10+
+1%2F35+%2B+1%2F14+=+1%2F10+
Multiply both sides by +14%2A35+
+14+%2B+35+=+490%2F10+
+49+=+49+
OK