SOLUTION: a car travel 300km at uniform rate.if the speed of the car had been 5km/h more, the journey would have taken 2 hours less.what is the speed of car?

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Question 941036: a car travel 300km at uniform rate.if the speed of the car had been 5km/h more, the journey would have taken 2 hours less.what is the speed of car?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the car's normal rate
Let +t+ = the car's time traveling at it's normal rate
(1) +300+=+s%2At+
(2) +300+=+%28+s+%2B+5+%29%2A%28+t+-+2+%29+
----------------------------
(2) +300+=+s%2At+%2B+5t+-+2s+-+10+
(2) +310+=+s%2At+%2B+5t+-+2s+
and
(1) +t+=+300%2Fs+
---------------------
Substitute (1) into (2)
(2) +310+=+300+%2B+1500%2Fs+-+2s+
(2) +1500%2Fs+-+2s+=+10+
(2) +1500+-+2s%5E2+=+10s+
(2) +2s%5E2+%2B+10s+-+1500+=+0+
(2) +s%5E2+%2B+5s+-+750+=+0+
(2) +%28+s+%2B+30+%29%2A%28+s+-+25+%29+=+0+ ( figured out by noting: +750+=+25%2A30+ )
+s+=+25+ ( can't use negative +30+ speed )
The car's speed in 25 km/hr
-------------------------
check:
(1) +300+=+25%2At+
(1) +t+=+12+ hrs
and
(2) +300+=+%28+s+%2B+5+%29%2A%28+t+-+2+%29+
(2) +300+=+%28+25+%2B+5+%29%2A%28+12+-+2+%29+
(2) +300+=+30%2A10+
(2) +300+=+300+
OK