Two trains, each having a speed of 30 km/h, are headed at each other on the same 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, the bird flies directly back to the first train, and so forth. What is the total distance the bird travels before the trains collide? Please show the calculation also......thank you.

To solve this problem, we need to determine how long it takes for the two trains to collide and then calculate the distance the bird travels during that time. Let's break it down step by step.

Understanding the Scenario

We have two trains moving towards each other, each at a speed of 30 km/h. The distance between them is 60 km. A bird flies back and forth between the two trains at a speed of 60 km/h. The key to solving this problem is to find out how long it takes for the trains to collide.

Calculating the Time Until Collision

First, we need to find the combined speed of the two trains. Since they are moving towards each other, we can add their speeds:

• Speed of Train 1 = 30 km/h
• Speed of Train 2 = 30 km/h
• Combined Speed = 30 km/h + 30 km/h = 60 km/h

Next, we can use the formula for time, which is:

Time = Distance / Speed

Substituting the values we have:

Time = 60 km / 60 km/h = 1 hour

Calculating the Distance Traveled by the Bird

Now that we know the trains will collide in 1 hour, we can calculate how far the bird travels in that time. The bird flies at a speed of 60 km/h. Using the same formula for distance:

Distance = Speed × Time

Substituting the bird's speed and the time until the trains collide:

Distance = 60 km/h × 1 hour = 60 km

Final Result

Therefore, the total distance that the bird travels before the trains collide is 60 kilometers.

This problem illustrates the concept of relative speed and how objects moving towards each other can be analyzed effectively. The bird's constant back-and-forth flight adds an interesting layer, but ultimately, the time until collision is determined by the trains' speeds and the initial distance between them.