Two trains 150 kilometer apart travel towards each other on parallel tracks, each moving at 25 kilometer per hour. A bird flies back and forth between the two trains at 50 kilometer per hour, until the train passes each other how far does the bird fly?
Let's break down the problem step-by-step:
1. The two trains are 150 kilometers apart.
2. Each train is moving towards each other at a speed of 25 kilometers per hour.
3. The relative speed of the two trains is the sum of their individual speeds, which is 25 + 25 = 50 kilometers per hour.
4. The time taken for the trains to pass each other is determined by the formula: time = distance / speed. Since the total distance is 150 kilometers and the relative speed is 50 kilometers per hour, the time taken is 150 / 50 = 3 hours.
5. The bird is flying back and forth between the two trains at a speed of 50 kilometers per hour, equivalent to the relative speed of the two trains.
6. Since the bird flies for 3 hours, the total distance covered by the bird is 50 * 3 = 150 kilometers.
Therefore, the bird flies a distance of 150 kilometers before the trains pass each other.
To find out how far the bird flies, we need to determine the time it takes for the two trains to pass each other. Since both trains are moving towards each other, their speeds are additive.
The combined speed of the two trains is 25 km/h + 25 km/h = 50 km/h.
To calculate the time it takes for the two trains to pass each other, we can use the formula:
time = distance / speed
The distance between the two trains is given as 150 km and the combined speed is 50 km/h. Plugging these values into the formula, we have:
time = 150 km / 50 km/h = 3 hours
Now that we know it takes 3 hours for the trains to pass each other, we can calculate how far the bird flies during this time.
The bird is flying between the two trains at 50 km/h. So, the distance the bird covers in 1 hour is 50 km.
Therefore, the total distance the bird flies in 3 hours is:
distance = speed × time = 50 km/h × 3 hours = 150 km
Hence, the bird flies 150 kilometers.
the trains are closing at 50 kph (25 + 25)
they start 150 km apart, so it takes them 3 hr to meet (and pass)
the bird flies for 3 hr at 50 kph, so it flies 150 km