The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12 h more than the airplane. Determine the average speeds of the train and the airplane.

Answer

Average speed of the train = 90 km/h and average speed of the airplane = 360 km/h.

Explanation:-

If speed of train = x then the speed of airplane = 4x km/h and we have the 2 equations

x = 1440 / (t + 12) (t = time taken by the train)

4x = 1440 / t ... (1) (t = time taken by train)

Multiply the first equation by 4:-

4x = 5760 / (t + 12) ... (2)

Combining equations (1) and (2) : -

1440 / t = 5760 / (t + 12)

Cross multiplying:-

5760t = 1440t + 17,280

4320t = 17,280

t = 17280/4320

t = 4 hours

speed of train = 1440 / (4 + 12) = 90 km/h and speed of plane = 4*90 = 360 km/h.