SOLUTION: A company buys a new pump that can pump 10.0 gal./min faster than its old one. It can fill the company's 500.0 gallon tank 15.0 minutes faster than the old pump. What was the speed

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A company buys a new pump that can pump 10.0 gal./min faster than its old one. It can fill the company's 500.0 gallon tank 15.0 minutes faster than the old pump. What was the speed      Log On


   

Question 1074537: A company buys a new pump that can pump 10.0 gal./min faster than its old one. It can fill the company's 500.0 gallon tank 15.0 minutes faster than the old pump. What was the speed of the old pump?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = the rate in gal/min of the NEW pump
+r+-+10+ = the rate in gal/min of the OLD pump
Let +t+ = time in minutes to to fill the tank with NEW pump
+t+%2B+15+ = time in minutes to fill the tank with OLD pump
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[ gallons ] / [ rate in gal/min ] = [ time in minutes ]
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Equation for old tank:
(1) +500+%2F+%28+r+-+10+%29+=+t+%2B+15+
Equation for the new tank:
(2) +500+%2F+r+=+t+
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Substitute (2) into (1)
(1) +500+%2F+%28+r+-+10+%29+=+500%2Fr+%2B+15+
Multiply both sides by +r%2A%28+r+-+10+%29+
(1) +500r+=+500%2A%28+r+-+10+%29+%2B+15%2Ar%2A%28+r+-+10+%29+
(1) +500r+=+500r+-+5000+%2B+15r%5E2+-+150r+%29+
(1) +15r%5E2+-+150r+-+5000+=+0+
(1) +3r%5E2+-+30r+-+1000+=+0+
+r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-30+
+c+=+-1000+
+r+=+%28+-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%2A3%2A%28-1000%29+%29%29%2F%282%2A3%29+
+r+=+%28+30+%2B-+sqrt%28+900+%2B+12000+%29%29%2F+6+
+r+=+%28+30+%2B-+sqrt%28+12900+%29%29%2F+6+
+r+=+%28+30+%2B+113.58+%29+%2F+6+
+r+=+143.58+%2F+6+
+r+=+23.93+
and
+r+-+10+=+13.93+
The speed of the old pump is 13.93 gal/min
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check answer:
(2) +500+%2F+r+=+t+
(2) +t+=+500%2F23.93+
(2) +t+=+20.89+
and
(1) +500+%2F+%28+r+-+10+%29+=+t+%2B+15+
(1) +500+%2F+13.93+=+t+%2B+15+
(1) +35.89+=+t+%2B+15+
(1) +t+=+20.89+
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Looks good, but check all my math and
get another opinion if you like