A runner is jogging at a steady 2.3 km/hr.
When the runner is 2.6 km from the finish
line, a bird begins flying from the runner to
the finish line at 13.8 km/hr (6 times as fast
as the runner). When the bird reaches the
finish line, it turns around and flies back to
the runner.
How far does the bird travel?

To solve this problem, we can use the fact that the bird is flying back and forth between the runner and the finish line until the runner reaches the finish line. Since the bird is flying at a constant speed, we can calculate the total time the runner takes to reach the finish line and determine how far the bird travels during that time.

### Step-by-Step Solution:

1. **Runner's Time to Reach the Finish Line**:
   - The runner is jogging at a speed of 2.3 km/h.
   - The distance from the runner to the finish line is 2.6 km.
   
   The time it takes for the runner to reach the finish line is:
   \[
   \text{Time for runner} = \frac{\text{Distance}}{\text{Speed}} = \frac{2.6 \, \text{km}}{2.3 \, \text{km/h}} \approx 1.13 \, \text{hours}.
   \]

2. **Bird's Distance Calculation**:
   - The bird is flying at 13.8 km/h, which is 6 times the speed of the runner.
   - The bird flies for the same amount of time that the runner takes to reach the finish line (1.13 hours).

   The distance the bird travels is:
   \[
   \text{Distance traveled by the bird} = \text{Speed of bird} \times \text{Time} = 13.8 \, \text{km/h} \times 1.13 \, \text{hours} \approx 15.59 \, \text{km}.
   \]

### Conclusion:
The bird travels approximately **15.59 km** during the time it takes the runner to reach the finish line.

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A runner is jogging at a steady 2.3 km/hr. When the runner is 2.6 km from the finish line, a bird begins flying from the runner to the finish line at 13.8 km/hr (6 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner. How far does the bird travel?

Solve a relative motion problem where a bird flies between a runner and the finish line. The runner jogs at 2.3 km/h, and the bird flies 6 times faster at 13.8 km/h. Learn how to calculate the total distance traveled by the bird using the time-distance-speed formula. Suitable for Grades 8-10 students.

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