Question

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

Answer 1

Answer:

The average speed of the train is 45 km/h

Explanation:

Speed

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

$\displaystyle v=\frac{d}{t}$

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:

$\displaystyle t_1=\frac{d_1}{v_1}$

$\displaystyle t_1=\frac{1/3x}{25}$

$\displaystyle t_1=\frac{x}{75}$

Now the rest of the distance:

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

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

$\displaystyle t_2=\frac{d_2}{v_2}$

$\displaystyle t_2=\frac{2/3x}{75}$

$\displaystyle t_2=\frac{2x}{225}$

The total time is:

$\displaystyle t_t=\frac{x}{75}+\frac{2x}{225}$

$\displaystyle t_t=\frac{3x}{225}+\frac{2x}{225}$

$\displaystyle t_t=\frac{5x}{225}$

Simplifying:

$\displaystyle t_t=\frac{x}{45}$

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

$\displaystyle \bar v=\frac{x}{\frac{x}{45}}$

Simplifying:

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

The average speed of the train is 45 km/h