Two trains, each having a speed of 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train, it flies directly back to the first train, and so forth. What is the total distance the bird travels?
Best to draw a timeline with a diagram for each key moment in time. Let us know if you get stuck.
How long before the trains meet? How long is the bird in the air? How far can the bird fly in that time?
60 km
The bird is traveling for an hour because it takes the two trains 60 minutes to travel 30 km to the point of collision. Since the bird has been flying for 60 minutes and it traveles 1 km per minute, (60 min) * (1 km / min) = 60 km
Well, it seems like the bird is having a lot of fun flying back and forth between the trains. It's probably enjoying the view of the choo-choo trains from high up in the sky.
Now, let's calculate how long the bird is in the air. Since the trains are traveling towards each other at a combined speed of 30 km/h + 30 km/h = 60 km/h, it will take them 60 km / 60 km/h = 1 hour to meet.
Since the bird flies off when the trains are 60 km apart and it takes 1 hour for them to meet, the bird is traveling for 1 hour.
Now, let's calculate how far the bird can fly in that time. We know that the bird's speed is 60 km/h, and it has been flying for 1 hour. So, the total distance the bird travels is 60 km/h * 1 hour = 60 km.
So, there you have it! The bird travels a total distance of 60 km. I hope it enjoyed its little flying adventure!
To solve this problem, let's break it down into steps:
Step 1: Find the time it takes for the trains to meet.
The trains are traveling towards each other at a combined speed of 30 km/h + 30 km/h = 60 km/h. The distance between them is 60 km. We can use the formula Speed = Distance / Time to find the time it takes for the trains to meet.
Time = Distance / Speed
Time = 60 km / 60 km/h
Time = 1 hour
Step 2: Find the distance the bird can fly in that time.
Since the bird starts flying when the trains are 60 km apart and it takes 1 hour for the trains to meet, the bird is in the air for 1 hour. The bird's speed is 60 km/h, so we can calculate the distance the bird can fly in that time.
Distance = Speed * Time
Distance = 60 km/h * 1 hour
Distance = 60 km
Therefore, the bird travels a total distance of 60 km.
To solve this problem, let's break it down into key moments in time and analyze the distances involved.
First, let's determine how long before the trains meet. The trains are initially 60 km apart and are moving towards each other at a combined speed of 30 km/h + 30 km/h = 60 km/h. Therefore, it will take 60 km / 60 km/h = 1 hour for the trains to meet.
Next, let's calculate the total time the bird is in the air. Since the trains meet after 1 hour, the bird is flying for the same duration. So, the bird is in the air for 1 hour.
Now, let's find out how far the bird can fly in that time. The bird flies at a speed of 60 km/h, so in 1 hour, it can cover a distance of 60 km/h * 1 hour = 60 km.
Therefore, the total distance the bird travels is 60 km.
To visualize this scenario, you can draw a timeline with a diagram for each key moment in time. Start by drawing two trains 60 km apart, then label the distances covered by each train in 1-hour increments until they meet. Also, draw the bird's path from one train to the other and back. This can help you better understand the distances and visualize the solution.