SOLUTION: Jason travels 2000 km by train and 400 km by car. The train is twice as fast as the car. If his total travel time is 20 hours, find the speed of the train.

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Question 1027283: Jason travels 2000 km by train and 400 km by car. The train is twice as fast as the car. If his total travel time is 20 hours, find the speed of the train.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours for the car
+20+-+t+ = time in hours for the train
Let +s+ = the speed of the car in km/hr
+2s+ = the speed of the train in km/hr
------------------------------------
Equation for the car:
(1) +400+=+s%2At+
Equation for the train:
(2) +2000+=+2s%2A%28+20+-+t+%29+
------------------------
(1) +s+=+400%2Ft+
Substitute (1) into (2)
(2) +2000+=+2%2A%28+400%2Ft+%29%2A%28+20+-+t+%29+
(2) +2000+=+2%2A%28+8000%2Ft+-+400+%29+
(2) +2000+=+16000%2Ft+-+800+
(2) +20+=+160%2Ft+-+8+
(2) +160%2Ft+=+28+
(2) +t+=+160%2F28+
(2) +t+=+40%2F7+
-------------------
(1) +400+=+s%2At+
(1) +400+=+s%2A%28+40%2F7+%29+
(1) +2800+=+40s+
(1) +s+=+70+
and
+2s+=+2%2A70+
+2s+=+140+
the speed of the train is 140 km/hr
(2) +2000+=+2s%2A%28+20+-+t+%29+
(2) +2000+=140%2A%28+20+-+t+%29+
(2) +100%2F7+=+20+-+t+
(2) +t+=+20+-+100%2F7+
(2) +t+=+140%2F7+-+100%2F7+
(2) +t+=+40%2F7+
OK