When the two 10 km/hr bikes (in the drawing below) are 20 km apart, a bee begins flying from one wheel to the other at a steady speed of 30 km/hr. When it gets to the wheel it abruptly turns around and flies back to touch the first wheel, then turns around and keeps repeating the back-and-forth trip until the bikes meet, and the bee gets squished!

How many kilometers did the bee travel in its total back-and forth trips? Justify your answer.

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To find out how many kilometers the bee traveled in its total back-and-forth trips, let's break down the problem and analyze it step by step.

We are given the following information in the problem:
- The bikes are moving towards each other at a speed of 10 km/hr each.
- Initially, the bikes are 20 km apart.

To solve this problem, we need to determine the time it takes for the bikes to meet and, consequently, the time it takes for the bee to get squished.

Let's calculate the time it takes for the bikes to meet. We can use the formula:

Time = Distance / Speed

Since both bikes are moving towards each other, their relative speed is the sum of their individual speeds. Therefore, the relative speed of the two bikes is:

Relative Speed = Speed of Bike 1 + Speed of Bike 2 = 10 km/hr + 10 km/hr = 20 km/hr

Now, we can find the time it takes for the bikes to meet by using the formula:

Time = Distance / Speed = 20 km / 20 km/hr = 1 hour

We know that the bee starts flying from one wheel to the other when the bikes are 20 km apart. From that point on, the bee keeps traveling back and forth until the bikes meet.

Since the bee's speed is 30 km/hr, we can calculate the distance the bee travels in one hour:

Distance = Speed x Time = 30 km/hr x 1 hour = 30 km

Therefore, the bee travels 30 km in one hour.

Since the bee travels 30 km in one hour and the bikes meet after 1 hour, the bee would have completed one back-and-forth trip.

So, the total distance the bee travels in its back-and-forth trips would be:

Total Distance = Distance per trip x Number of trips

Since the bee completes one trip in one hour, the number of trips is equal to the time it takes for the bikes to meet (1 hour).

Total Distance = 30 km/trip x 1 trip = 30 km

Hence, the bee travels a total distance of 30 kilometers in its back-and-forth trips before getting squished.