SOLUTION: The Austin Healthmate 400 can purify the air in a conference hall in 15 fewer minutes than it takes the Airgle 750 Air Purifier to do the same job. Together the two machines can pu

Algebra ->  Rate-of-work-word-problems -> SOLUTION: The Austin Healthmate 400 can purify the air in a conference hall in 15 fewer minutes than it takes the Airgle 750 Air Purifier to do the same job. Together the two machines can pu      Log On


   

Question 737108: The Austin Healthmate 400 can purify the air in a conference hall in 15 fewer minutes than it takes the Airgle 750 Air Purifier to do the same job. Together the two machines can purify the air in the conference hall in 10 minutes. How long would it take each machine, working alone, to purify the air in the room?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in minutes for Airgle 750 to do the job
+t+-+15+ = time for A. H. 400 to do job
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Add their rate of purifying:
( 1 job ) / ( t min ) + ( 1 job ) / ( t - 15 min ) = 1 / 10 min
+1%2Ft+%2B+1%2F%28+t-15+%29+=+1%2F10+
Multiply both sides by +t%2A%28+t-15+%29%2A10+
+10%2A%28+t-15+%29+%2B+10t+=+t%2A%28+t-15+%29+
+10t+-+150+%2B+10t+=+t%5E2+-+15t+
+t%5E2+-+35t+%2B+150+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-35+
+c+=+150+
+t+=+%28+-%28-35%29+%2B-+sqrt%28+%28-35%29%5E2+-+4%2A1%2A150+%29%29+%2F+%282%2A1%29+
+t+=+%28+35+%2B-+sqrt%28+1225+-+600+%29%29+%2F+2+
+t+=+%28+35+%2B+sqrt%28+625+%29%29+%2F+2+
+t+=+%28+35+%2B+25+%29+%2F+2+
+t+=+30+
and, also
+t+=+%28+35+-+25+%29+%2F+2+
+t+=+5+ ( reject this solution )
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+t+-+15+=+15+
It took 30 minutes for Airgle 750 to do the job
It took 15 minutes for A. H. 400 to do job
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check answers:
+1%2Ft+%2B+1%2F%28+t-15+%29+=+1%2F10+
+1%2F30+%2B+1%2F15+=+1%2F10+
+1%2F30+%2B+2%2F30+=+3%2F30+
+3%2F30+=+3%2F30+
OK