Question

A train travels the first 30 km of 120 km track with a uniform speed of 30 km/h. What should be the speed of the train to cover the remaining distance of track so that average speed will be 60km/h for the whole journey?

Answer 1

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Time taken to travel first 30 km

t1 = $\frac{30km}{30km/h}$

= 1 h

Let V = speed of the train with which it travels the remaining distance of 90 km.

Time taken to travel remaining distance (90km)

=》 t2 = $\frac{90}{V}$

=》Average speed = $\frac{Total\:Distance}{Total\:Time\:Taken}$

=》Average speed = $\frac{120}{t1 + t2}$ ........... ☝

=》 Average Speed = 60 km/h (given in the question )

Put the value of t1 and t2 in the equation ☝

=》 60 = $\frac{120}{1 + \frac{90}{V} }$

=》 1 + $\frac{90}{V}$ = $\frac{120}{60}$

=》 1 + $\frac{90}{V}$ = 2 OR

=》 V = 90 km/h

So, the speed by which the train needs to travel to continue its average speed of 60km/h is 90km/h .

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Hope this helps. . . . . . . . ☺☺