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:
[tex]v_{1}\cdot t_{1} = v_{2}\cdot t_{2}[/tex] (1)
Where:
[tex]v_{1}, v_{2}[/tex] - Average speeds of the express train and the normal train, in kilometers per hour.
[tex]t_{1}, t_{2}[/tex] - Travel times of the express train and the normal train, in hours.
In addition, there is the following relationship between average speeds:
[tex]v_{1} = v_{2} + 90[/tex] (2)
By (2) in (1), we have the following expression for the average speed of the normal train:
[tex](v_{2} + 90) \cdot t_{1} = v_{2}\cdot t_{2}[/tex]
[tex]90\cdot t_{1} = v_{2} \cdot (t_{2} - t_{1})[/tex]
[tex]v_{2} = \frac{90\cdot t_{1}}{t_{2}-t_{1}}[/tex]
If we know that [tex]t_{1} = 4\,h[/tex] and [tex]t_{2} = 10\,h[/tex], then the average speed of the normal train is:
[tex]v_{2} = 90\cdot \left(\frac{4\,h}{10\,h - 4\,h} \right)[/tex]
[tex]v_{2} = 60\,\frac{km}{h}[/tex]
The speed of the normal train is 60 kilometers per hour.
