Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards the other at a speed of 75 km/h. Upon reaching the other train, the fly turns around and continues towards the first train. How many kilometers does the fly travel before getting squashed in the collision of the two trains?

So the distance between the two trains is changing at a rate of 100 km/h, (the sum of their speeds)

so it will take them 100/100 or 1 hour to collide.

In the meantime, the fly is merrily flying back and forth at 75 km/h, so in the 1 hour it would have simply traveled 75 km.

Notice we ignored the fact that the fly has to decelerate and accelerate at each turn.

Well, it seems like the fly is quite the daredevil! Let's see if we can calculate how far it travels before meeting its squishy fate.

First, we should figure out how long it takes for the trains to collide. Since they are 100 km apart and each traveling at 50 km/h, they are closing the gap at a combined speed of 100 km/h. So, it would take them one hour to collide.

During that hour, the fly is flying towards the other train at 75 km/h. In one hour, it would cover a distance of 75 km. However, since the two trains are moving towards each other, the fly only needs to fly for half an hour before reaching the other train. So, the fly travels 75 km for half an hour.

After reaching the other train, the fly turns around and heads back towards the first train. This means it will cover the same distance of 75 km again.

So, in total, the fly travels 75 km + 75 km = 150 km before its unfortunate encounter with the collision. That's quite a journey for a little fly!

To find out how many kilometers the fly travels before getting squashed, we need to calculate the time it takes for the two trains to collide.

Let's first calculate the time it takes for the two trains to collide:

The total distance the two trains need to cover to meet is 100 km. The combined speed of the two trains is 50 km/h + 50 km/h = 100 km/h.

Using the formula Distance = Speed × Time, we can find the time it takes for the two trains to collide:

100 km = 100 km/h × Time
Time = 1 hour

Therefore, it takes 1 hour for the two trains to collide.

Now let's calculate how far the fly travels during that time:

The fly's speed is 75 km/h. Since it flies for 1 hour before the collision, we can calculate the distance it travels using the formula Distance = Speed × Time:

Distance = 75 km/h × 1 hour
Distance = 75 km

Therefore, the fly travels 75 kilometers before getting squashed in the collision of the two trains.

To solve this problem, we need to find out how long it takes for the two trains to collide. Once we have the time, we can determine the distance traveled by the fly.

Let's break down the problem step by step:

Step 1: Find the relative speed of the trains
Since the trains are approaching each other, we need to find their combined speed. Adding their individual speeds gives us:
Relative speed = Speed of train 1 + Speed of train 2
Relative speed = 50 km/h + 50 km/h
Relative speed = 100 km/h

Step 2: Calculate the time to collision
To determine the time it takes for the two trains to collide, we can use the formula: time = distance / speed
Distance = 100 km (given in the question)
Speed = relative speed = 100 km/h (calculated in Step 1)

Therefore, time = 100 km / 100 km/h = 1 hour

Step 3: Calculate the distance traveled by the fly
Now that we know the time it takes for the trains to collide (1 hour), we can calculate the distance traveled by the fly. To calculate the distance, we can use the formula: distance = speed × time

Speed of the fly = 75 km/h (given in the question)
Time = 1 hour (calculated in Step 2)

Therefore, distance = 75 km/h × 1 hour = 75 km

Hence, the fly travels a distance of 75 kilometers before the collision occurs.