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.