Question

An express train travel from A to B for 4 hours. A normal train travel from B to A for 10 hours. Both of them started at the same time. The average speed of the express train is greater than the average speed of the normal train 90km/h. Find the average speed of the normal train?

Answer 1

Answer:

The speed of the normal train is 60 kilometers per hour.

Step-by-step explanation:

Let suppose that both trains move at constant speed and cover the same distance. Then, we have the following identity:

$v_{1}\cdot t_{1} = v_{2}\cdot t_{2}$ (1)

Where:

$v_{1}, v_{2}$ - Average speeds of the express train and the normal train, in kilometers per hour.

$t_{1}, t_{2}$ - Travel times of the express train and the normal train, in hours.

In addition, there is the following relationship between average speeds:

$v_{1} = v_{2} + 90$ (2)

By (2) in (1), we have the following expression for the average speed of the normal train:

$(v_{2} + 90) \cdot t_{1} = v_{2}\cdot t_{2}$

$90\cdot t_{1} = v_{2} \cdot (t_{2} - t_{1})$

$v_{2} = \frac{90\cdot t_{1}}{t_{2}-t_{1}}$

If we know that $t_{1} = 4\,h$ and $t_{2} = 10\,h$, then the average speed of the normal train is:

$v_{2} = 90\cdot \left(\frac{4\,h}{10\,h - 4\,h} \right)$

$v_{2} = 60\,\frac{km}{h}$

The speed of the normal train is 60 kilometers per hour.