Answer :
The distance covered by car is equal to (assuming it is moving by uniform motion) the product between the car's speed and the time of the car ride, 4 h:
[tex]S_c = v_c t_c [/tex]
where
[tex]v_c [/tex] is the car's speed
[tex]t_c = 4 h[/tex] is the duration of the car ride
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
[tex]S_t = v_t t_t[/tex]
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
[tex]S=255 km = S_c + S_t [/tex]
which becomes
[tex]255 = 4 v_c + 7 v_t[/tex] (1)
we also know that the train speed is 5 km/h greater than the car's speed:
[tex]v_t = 5 + v_c[/tex] (2)
If we put (2) into (1), we find
[tex]255 = 4v_c + 7(5+v_c)[/tex]
and if we solve it, we find
[tex]v_c = 20 km/h[/tex]
[tex]v_t = 25 km/h[/tex]
So, the car speed is 20 km/h and the train speed is 25 km/h.
[tex]S_c = v_c t_c [/tex]
where
[tex]v_c [/tex] is the car's speed
[tex]t_c = 4 h[/tex] is the duration of the car ride
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
[tex]S_t = v_t t_t[/tex]
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
[tex]S=255 km = S_c + S_t [/tex]
which becomes
[tex]255 = 4 v_c + 7 v_t[/tex] (1)
we also know that the train speed is 5 km/h greater than the car's speed:
[tex]v_t = 5 + v_c[/tex] (2)
If we put (2) into (1), we find
[tex]255 = 4v_c + 7(5+v_c)[/tex]
and if we solve it, we find
[tex]v_c = 20 km/h[/tex]
[tex]v_t = 25 km/h[/tex]
So, the car speed is 20 km/h and the train speed is 25 km/h.