15 seconds after the buzzer, the teacher still has 135 meters to go to the finish line. 32 seconds after he left the starting line, the teacher has only 50 meters more to run. 22 seconds after the buzzer, Usain is 189 meters from the finish line. 36 seconds after the buzzer, he is 42 meters from the finish line. Both people are running at a constant speed. determine the outcome of the race. explain your process.

Question

15 seconds after the buzzer, the teacher still has 135 meters to go to the finish line. 32 seconds after he left the starting line, the teacher has only 50 meters more to run. 22 seconds after the buzzer, Usain is 189 meters from the finish line. 36 seconds after the buzzer, he is 42 meters from the finish line. Both people are running at a constant speed. determine the outcome of the race. explain your process.

Answer 1

To determine the outcome of the race, we first need to find the rate at which each person is running. We can then use this information to calculate how far each person has run at specific time intervals.

Let's start by calculating the teacher's rate. Since the teacher has 135 meters left 15 seconds after the buzzer, we can find the teacher's speed by dividing the remaining distance by the time elapsed after the buzzer:

Teacher's speed = Distance / Time = 135 m / 15 s = 9 m/s

Next, let's calculate the rate at which Usain is running. After 22 seconds from the buzzer, Usain has 189 meters to go. Therefore, his speed can be calculated as:

Usain's speed = Distance / Time = 189 m / 22 s ≈ 8.59 m/s

We have the speed of both the teacher and Usain. Now, let's find their positions at specific time intervals to determine who reaches the finish line first.

32 seconds after leaving the starting line, the teacher has only 50 meters more to run. We can calculate the distance the teacher has covered by subtracting 50 meters from the original distance:

Teacher's distance covered = Total distance - Remaining distance = 135 m - 50 m = 85 m

Similarly, we can find Usain's distance covered after 32 seconds by subtracting the remaining distance from the total distance:

Usain's distance covered = Total distance - Remaining distance = 189 m - 50 m = 139 m

Now, let's calculate the positions of both runners at the finish line.

For the teacher:
Teacher's position = Distance covered + Remaining distance = 85 m + 0 m = 85 m

For Usain:
Usain's position = Distance covered + Remaining distance = 139 m + 0 m = 139 m

Comparing their positions, we can see that the teacher reaches the finish line first, as their position is 85 meters while Usain's position is still 139 meters away from the finish line.

In summary, based on the given information, the teacher wins the race, reaching the finish line before Usain.