Question

a) A train travels a distance with a speed of 40 km/h and returns with a speed of 60 km/h. Calculate the average speed of the train.

b) On a 60 km track, a train travels the first 30 km at a uniform speed of 30 km/h. How fast must a train travel the next 30 km so that the average speed is 40 km/hr for the entire trip?

Answer 1

a)

Let us assume that the train travels in one direction from location A to another location B. It then returns along the same route in the opposite direction from Point B to Point A.

Let the distance between Point A and Point B be D. The total distance is then 2D.

We know,

$Averagespeed=\frac{Totaldistancetraveled}{Totaltimetaken}$

Now we can write

$Averagespeed=\frac{2D}{(\frac{D}{40}+\frac{D}{60})}$

After solving

$Averagespeed=48$ km/h

Hence the average speed is 48 km/h

b)

Total distance traveled = 60 km

First 30 km it travels at speed 30 km/h. Time taken $=\frac{Distance}{Speed}=\frac{30}{30}=1$ h

Suppose the next 30 km is traveled at speed x km/h. Time taken = $\frac{30}{x}$ km/h

We know,

$Averagespeed=\frac{Totaldistancetraveled}{Totaltimetaken}$

Putting all the values

$40=\frac{60}{1+\frac{30}{x}}$

After solving

x = 60 km/h

Hence the train must have to travel the next distance with a speed 60 km/h