Question

A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would still have 40 km more to go to station B. Find:

A) The distance between the two stations;
B) The time it takes the train to travel from A to B according to the schedule;
C) The speed of the train when it's on schedule.

Answer 1

• A) 290 km
• B) 4 hours
• C) 72.5 km/h

Explanation:

Let distance be d and time t

At 75 km/h speed the distance is

• d = 75(t - 48 min) = 75(t - 48/60 hours)

At 50 km/h speed the distance is

• d = 50t + 40

Since the distance is same, we get the equation:

• 75(t - 48/60) = 50t + 40
• 75t - 75*4/5 = 50t + 40
• 75t - 60 = 50t + 40
• 75t - 50t = 40 + 60
• 25t = 100
• t = 4 hours

A) The distance between A and B

• d = 50*5 + 40 = 290 km

B) Time is

• 4 hours as found above

C) The speed = d/t

• Speed = 290/4 = 72.5 km/h