Two trains are traveling towards each other, starting 100 kilometers apart. One train travels at 40 kilometers per hour while the other travels at 60 kilometers per hour. The plane starts flying at 90 kilometers per hour, starting from the location of the faster train. Once the plane reaches the slow train, it turns around immediately and flies back. Once it reaches the fast train again, it turns around and flies towards the slow train, etc.
When the trains pass each other, how far will the plane have flown?
the trains are closing at 100 kph
... so it takes them 1 hr to pass
the plane flies 90 kph for 1 hr
To find out how far the plane will have flown when the trains pass each other, we need to calculate the time it takes for the trains to meet.
Let's consider the distances covered by the slower train (40 km/h) and the faster train (60 km/h) as a function of time. Assuming both trains starting from 100 km apart:
Distance covered by the slower train (dS) = 40t kilometers, where t is the time in hours.
Distance covered by the faster train (dF) = 60t kilometers.
Since the trains are traveling towards each other, the sum of their distances covered will equal the initial separation of 100 kilometers:
40t + 60t = 100.
Simplifying the equation:
100t = 100.
Dividing both sides of the equation by 100, we find:
t = 1 hour.
Therefore, it will take 1 hour for the trains to meet.
Next, let's determine how far the plane will have flown during this 1-hour period.
Since the plane starts flying from the location of the faster train, which is 100 kilometers from the slower train, the plane will be flying for 1 hour at a speed of 90 km/h:
Distance covered by the plane = 90 km/h * 1 hour = 90 kilometers.
Hence, when the trains pass each other, the plane will have flown 90 kilometers.