Question

A train is moving in a straight railway where it covered one third of the distance with

a speed of 25 km/h and the remaining distance was covered by a speed of 75 km
so the average speed of this train is......... km/h​

Answer 1

The average speed of the train is 45 km/h

Step-by-step explanation:

Speed

It's defined as the distance (d) per unit of time (t) traveled by an object. The formula is:

`\displaystyle v=(d)/(t)`

Let's call x the total distance covered by the train. It covered d1=1/3x with a speed of v1=25 km/h. The time taken is calculated solving for t:

`\displaystyle t_1=(d_1)/(v_1)`

`\displaystyle t_1=(1/3x)/(25)`

`\displaystyle t_1=(x)/(75)`

Now the rest of the distance:

d2 = x - 1/3x = 2/3x

Was covered at v2=75 km/h. Thus the time taken is:

`\displaystyle t_2=(d_2)/(v_2)`

`\displaystyle t_2=(2/3x)/(75)`

`\displaystyle t_2=(2x)/(225)`

The total time is:

`\displaystyle t_t=(x)/(75)+(2x)/(225)`

`\displaystyle t_t=(3x)/(225)+(2x)/(225)`

`\displaystyle t_t=(5x)/(225)`

Simplifying:

`\displaystyle t_t=(x)/(45)`

The average speed is the total distance divided by the total time:

`\displaystyle \bar v=(x)/((x)/(45))`

Simplifying:

`\boxed{\displaystyle \bar v=45\ km/h}`

The average speed of the train is 45 km/h