SOLUTION: The speed of an ordinary train is x km per hr and that of an express train is x+25 km per hr .(i) find the time taken by each train to cover a distance of 300km.(ii) if the ordina

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The speed of an ordinary train is x km per hr and that of an express train is x+25 km per hr .(i) find the time taken by each train to cover a distance of 300km.(ii) if the ordina      Log On


   

Question 1084609: The speed of an ordinary train is x km per hr and that of an express train is x+25 km per hr .(i) find the time taken by each train to cover a distance of 300km.(ii) if the ordinary train takes 2hrs more than the express train;calculate speed of the express train.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
Time for ordinary train:
+300+%2F+x+
Time for express train:
+300+%2F+x+%2B+25+
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(2)
+300%2Fx+=+300%2F%28+x+%2B+25+%29+%2B+2+
Multiply both sides by +x%2A%28+x+%2B+25+%29+
+300%2A%28+x+%2B+25+%29+=+300x+%2B+2%2Ax%2A%28+x+%2B+25+%29+
+300x+%2B+7500+=+300x+%2B+2x%5E2+%2B+50x+
+2x%5E2+%2B+50x+-+7500+=+0+
+x%5E2+%2B+25x+-+3750+=+0+
Use quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+25+
+c+=+-3750+
+x+=+%28+-25+%2B-+sqrt%28+25%5E2-4%2A1%2A%28-3750%29+%29%29%2F%282%2A1%29+
+x+=+%28+-25+%2B-+sqrt%28+625+%2B+15000+%29%29%2F2+
+x+=+%28+-25+%2B-+sqrt%28+15625+%29%29%2F2+
+x+=+%28+-25+%2B+125+%29+%2F+2+ ( can't use the negative sqrt )
+x+=+100%2F2+
+x+=+50+
and
+x+%2B+25+=+75+
The speed of the express train is 75 km/hr
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check:
+300%2Fx+=+300%2F%28+x+%2B+25+%29+%2B+2+
+300%2F50+=+300%2F75+%2B+2+
Multiply both sides by +150+
+3%2A300+=+2%2A300+%2B+300+
+900+=+600+%2B+300+
+900+=+900+
OK