SOLUTION: Help me to solve this problem: A plane takes 10 hours less to travel 1200 km than a train. If the plane travels six times as fast as the train, what was the speed of the plane? An

Question 1105322: Help me to solve this problem: A plane takes 10 hours less to travel 1200 km than a train. If the plane travels six times as fast as
the train, what was the speed of the plane? Answer is Speed of the train was 100 km/hr, the plane was 600 km/hr.
Found 3 solutions by Alan3354, josgarithmetic, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A plane takes 10 hours less to travel 1200 km than a train. If the plane travels six times as fast as
the train, what was the speed of the plane?
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P = plane's speed, T = train's speed in mi/hr
---
P = 6T

Sub for P

Multiply thru by 6T

etc
Answer by josgarithmetic(39613)   (Show Source): You can put this solution on YOUR website!
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A plane takes 10 hours less to travel 1200 km than a train. If the plane travels six times as fast as
the train, what was the speed of the plane?
----------------------------------------------------------------------------

Easier to assign variables as shown here:

SPEED TIME DISTANCE PLANE 6r 1200/(6r) 1200 TRAIN r 1200/r 1200 DIFFERENCE 10

You are really asked to find 6r but you can solve for r first.

Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.
The MENTAL solution is also possible:

If the plane travels six times as fast as the train, the train spends six times as long time as the plane: 6x hours for the train and x hours for the plane. The difference is 10 hours: 6x - x = 10 hours, according to the condition. Hence, 5x = 10 and x = = 2 hours. Having 2 hours for the plane, you momentarily determine its speed: = 600 km/hours, exactly as in your answer.

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