Question

Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. what is the speed of the train, if it is 5 km/h greater than the speed of the car?

Answer 1

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:
$S_c = v_c t_c$
where
$v_c$ is the car's speed
$t_c = 4 h$ 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:
$S_t = v_t t_t$

The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
$S=255 km = S_c + S_t$
which becomes
$255 = 4 v_c + 7 v_t$ (1)
we also know that the train speed is 5 km/h greater than the car's speed:
$v_t = 5 + v_c$ (2)

If we put (2) into (1), we find
$255 = 4v_c + 7(5+v_c)$
and if we solve it, we find
$v_c = 20 km/h$
$v_t = 25 km/h$

So, the car speed is 20 km/h and the train speed is 25 km/h.