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:
[tex]\displaystyle v=\frac{d}{t}[/tex]
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:
[tex]\displaystyle t_1=\frac{d_1}{v_1}[/tex]
[tex]\displaystyle t_1=\frac{1/3x}{25}[/tex]
[tex]\displaystyle t_1=\frac{x}{75}[/tex]
Now the rest of the distance:
d2 = x - 1/3x = 2/3x
Was covered at v2=75 km/h. Thus the time taken is:
[tex]\displaystyle t_2=\frac{d_2}{v_2}[/tex]
[tex]\displaystyle t_2=\frac{2/3x}{75}[/tex]
[tex]\displaystyle t_2=\frac{2x}{225}[/tex]
The total time is:
[tex]\displaystyle t_t=\frac{x}{75}+\frac{2x}{225}[/tex]
[tex]\displaystyle t_t=\frac{3x}{225}+\frac{2x}{225}[/tex]
[tex]\displaystyle t_t=\frac{5x}{225}[/tex]
Simplifying:
[tex]\displaystyle t_t=\frac{x}{45}[/tex]
The average speed is the total distance divided by the total time:
[tex]\displaystyle \bar v=\frac{x}{\frac{x}{45}}[/tex]
Simplifying:
[tex]\boxed{\displaystyle \bar v=45\ km/h}[/tex]
The average speed of the train is 45 km/h
