SOLUTION: 2. A train required 2 h longer to travel 500 km than a plane required to travel 1200 km. Find the speed of the train, if the plane travels 4 times as fast as the train.

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Question 593008: 2. A train required 2 h longer to travel 500 km than a plane required to travel 1200 km. Find the speed of the train, if the plane travels 4 times as fast as the train.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the train
+4s+ = the speed of the plane
Let +t+ = time for the plane
+t+%2B+2+ = time for the train
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Equation for the train:
(1) +500+=+s%2A%28+t+%2B+2+%29+
Equation for the plane:
(2) +1200+=+4s%2At+
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This is 2 equations and 2 unknowns,
so it's solvable
(1) +500+=+s%2At+%2B+2s+
and
(2) +s%2At+=+1200%2F4+
(2) +s%2At+=+300+
Substitute (2) into (1)
(1) +500+=+300+%2B+2s+
(1) +2s+=+200+
(1) +s+=+100+
The speed of the train is 100 km/hr
check:
(2) +1200+=+4s%2At+
(2) +1200+=+4%2A100%2At+
(2) +t+=+3+
and
(1) +500+=+s%2A%28+t+%2B+2+%29+
(1) +500+=+100%2A%28+3+%2B+2+%29+
(1) +500+=+100%2A5+
(1) +500+=+500+
OK