SOLUTION: a car traveled at 1280 mi at a certain speed. if the speed had been 16mph faster, the trip would have been made in 4hr less time. find the speed.

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Question 654575: a car traveled at 1280 mi at a certain speed. if the speed had been 16mph faster, the trip would have been made in 4hr less time. find the speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the car's actual speed in mi/hr
Let +t+ = the car's actual time in hours
given:
(1) +1280+=+s%2At+
(2) +1280+=+%28+s+%2B+16+%29%2A%28+t+-4+%29+
----------------------------
(2) +1280+=+s%2At+-+4s+%2B+16t+-+64+
(2) +1344+=+s%2At+-+4s+%2B+16t+
Substitute (1) into (2)
(2) +1344+=+1280+-+4s+%2B+16t+
(2) +16t+=+4s+%2B+64+
And, from (1)
(1) +s+=+1280%2Ft+
Plug this back into (2)
(2) +16t+=+4%2A%28+1280%2Ft+%29+%2B+64+
(2) +16t%5E2+=+5120+%2B+64t+
(2) +t%5E2+-+4t+-+320+=+0+
I can solve this by inspection
(2) +%28+t+-+20+%29%2A%28+t+%2B+16+%29+
+t+=+20+ ( ignore +t+=+-16+, can't have negative time )
Plug this result back into (1)
(1) +1280+=+s%2A20+
(1) +s+=+64+
The car's speed is 64 mi/hr
check:
(2) +1280+=+%28+64+%2B+16+%29%2A%28+20+-4+%29+
(2) +1280+=+80%2A16+
(2) +1280+=+1280+
OK