A train covers half the distance of its journey with a speed 20 m s-1 and the other half with a speed of 40 m s-1. The average speed of the train during the whole journey is
A. 25 m s-1
B. 27 m s-1
C. 30 m s-1
D. 32 m s-1
E. 35 m s-1
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Let the total distance travelled by the train be d and the time taken for it to complete the first half and second half of the journey be t1 and t2 respectively. The distance travelled each half-journey is d/2 and it is the product of their respective travelling velocity and time taken.
For the first half-journey,
For the second half-journey,
Combining the above two equations, we get
Now we have the relationship between t1 and t2, we can eliminate one of them from our calculations. For convenience, let us state the d in terms of t2 and find the average speed, which is the total distance travelled divided by the total time taken.
Rounding off to the nearest integer, we have 27 m s-1.
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Question source: Malaysia National Physics Competition 2007 (Secondary Level)