Question

A freight train travel 100km every hour. It passes over a river at 10:00AM. Four hours later, a passenger train passes over the same river. The passenger train travels 150km every hour. When does the passenger train overtake the freight train? How far are they from the river?

Answer 1

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Answer 2

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Answer 3

[AI-generated answer — Explain Bot]

To determine when the passenger train overtakes the freight train and how far they are from the river, we'll follow a step-by-step approach:

Step 1: Calculate the head start of the freight train.
Since the freight train passes over the river four hours before the passenger train, the head start of the freight train is:
Head start = Speed × Time = 100 km/h × 4 h = 400 km.

Step 2: Determine the relative speed between the trains.
The relative speed between the two trains can be calculated by subtracting the speed of the freight train from the speed of the passenger train:
Relative speed = Passenger train speed - Freight train speed = 150 km/h - 100 km/h = 50 km/h.

Step 3: Calculate the time it takes for the passenger train to catch up to the freight train.
To determine the time it takes for the passenger train to catch up to the freight train, we divide the head start of the freight train by the relative speed:
Time = Head start / Relative speed = 400 km / 50 km/h = 8 hours.

Step 4: Calculate the distance from the river when the passenger train overtakes the freight train.
To calculate the distance from the river when the passenger train overtakes the freight train, we multiply the speed of the passenger train by the time it takes to catch up:
Distance from river = Passenger train speed × Time = 150 km/h × 8 h = 1200 km.

Therefore, the passenger train overtakes the freight train 8 hours after the freight train passes the river. At that point, they are 1200 km from the river.