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}__Solution__

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The answer is B.

Let the total distance travelled by the train be

For the first half-journey,

For the second half-journey,

Combining the above two equations, we get

Now we have the relationship between

Rounding off to the nearest integer, we have 27 m s

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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*t*_{1}and*t*_{2}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

*t*_{1 }and*t*_{2}, we can eliminate one of them from our calculations. For convenience, let us state the*d*in terms of*t*_{2}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}.Hide solution <<

**Question source:**Malaysia National Physics Competition 2007 (Secondary Level)

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