SOLUTION: A car travels 1500 miles at a certian speed. If the speed had been 10 mph faster, the trip could have been made in 5 hours less time. Find the speed

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Question 562875: A car travels 1500 miles at a certian speed. If the speed had been 10 mph faster, the trip could have been made in 5 hours less time. Find the speed
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time for the trip in hours
at speed +s+ in mi/hr
given:
(1) +1500+=s%2At+
and
(2) +1500+=+%28+s+%2B+10+%29%2A%28+t+-+5+%29+
(2) +1500+=+s%2At+%2B+10t+-+5s+-+50+
Substitute (1) into (2)
(2) +1500+=+1500+%2B+10t+-+5s+-+50+
(2) +10t+-+5s+-+50+=+0+
and
(1) +t+=+1500%2Fs+
(2) +10%2A%281500%2Fs%29+-+5s+-+50+=+0+
(2) +15000+-+5s%5E2+-+50s+=+0+
(2) +5s%5E2+%2B+50s+-+15000+=+0+
(2) +s%5E2+%2B+10s+-+3000+=+0+
Use quadratic equation
+s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+10+
+c+=+-3000++
+s+=+%28-10+%2B-+sqrt%28+10%5E2-4%2A1%2A%28-3000%29+%29%29+%2F+%282%2A1%29+
+s+=+%28-10+%2B-+sqrt%28+100+%2B+12000+%29%29+%2F+2+
+s+=+%28-10+%2B-+sqrt%28+12100+%29%29+%2F+2+
+s+=+%28-10+%2B+110%29+%2F+2+
+s+=+100%2F2+
+s+=+50+ ( I can ignore the (-) root )
The speed is 50 mi/hr
check answer:
(1) +1500+=s%2At+
(1) +1500+=+50t+
(1) +t+=+30+
and
(2) +1500+=+%28+50+%2B+10+%29%2A%28+30+-+5+%29+
(2) +1500+=+60%2A25+
(2) +1500+=+1500+
OK