Question

A passenger train left Austin, Texas at 12:00 PM bound for Dallas, exactly 210 miles away; it traveled at a steady 50 miles per hour. At the same time, a freight train left from Dallas headed for Austin at a steady 20 miles per hour. At the same time a fly leaped from the nose of the passenger train and flew along the track at 100 miles per hour. When the fly touched the nose of the oncoming freight train, she turned around and flew back at 100 miles per hour, when she reached the nose of the passenger train, she instantly turned and flew back toward the freight train. She continued turning and flying until the trains collided.1. After how long did the trains collide?2. How long before the fly reached the oncoming freight train?3. How far had the fly flown before the trains collided?

Answer 1

The passenger and freight trains collide after 3 hours. The fly reaches the oncoming freight train after 2.1 hours. The fly flies 300 miles before the trains collide.

Step-by-step explanation:

To solve this problem, we can use the formula: time = distance / speed. In this case, the distance between Austin and Dallas is 210 miles, and the passenger train travels at a speed of 50 mph, while the freight train travels at a speed of 20 mph.

1. The time it takes for the trains to collide can be calculated by dividing the distance between them by the combined speed of both trains: 210 miles / (50 mph + 20 mph) = 210 miles / 70 mph = 3 hours. Therefore, the trains collide after 3 hours.

2. The time it takes for the fly to reach the oncoming freight train can be calculated by dividing the distance between the fly and the freight train by the fly's speed: 210 miles / 100 mph = 2.1 hours. Therefore, the fly reaches the freight train after 2.1 hours.

3. The distance the fly flies before the trains collide can be calculated by multiplying the fly's speed by the time it takes for the trains to collide: 100 mph * 3 hours = 300 miles. Therefore, the fly flies 300 miles before the trains collide.

Answer 2

1. 3 hours
2. 1 hour 45 minutes
3. 300 miles

Step-by-step explanation:

1. The trains are moving toward each other at a total speed of 50 +20 = 70 miles per hour. Together, they cover the 210 mile distance in ...

time = distance/speed

time = 210 mi/(70 mi/h) = 3 h

The trains collide after 3 hours.

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2. The fly is closing with the freight train at a speed of 100 +20 = 120 miles per hour. Together, the fly and the train cover the initial 210 mile distance in ...

(210 mi)/(120 mi/h) = 7/4 h = 1 hour 45 minutes

The fly first meets the oncoming freight train after 1 h 45 min.

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3. The fly is flying for all three hours before the trains collide, so, at 100 miles per hour, will fly 300 miles.