Question

Jordan and Amari run a 200-meter race, and Jordan wins by 23 meters. They decide to run the 200 meter race again with Jordan starting 23 meters behind the starting

line.
a. Assuming both runners run at the same pace as they did in the first race, who wins the second race?

Answer 1

If Jordan and Amari run at the same pace in the second 200-meter race as they did in the first, with Jordan starting 23 meters behind, Jordan still wins. This is assuming that the extra distance Jordan runs is equivalent to the lead he previously established.

Step-by-step explanation:

Given that Jordan wins by 23 meters in the first 200-meter race, this sets the stage for the second race where Jordan starts 23 meters behind the starting line. Assuming Jordan and Amari maintain the same pace in the second race as they did in the first, the situation is effectively the same. Therefore, Jordan would need to cover 223 meters (200 + 23) while Amari would cover 200 meters, which is the same relative difference as the outcome of the first race.

For the second race, both runners start and finish at the same time, Jordan still wins. This is because Jordan is starting behind by the exact distance he beat Amari in the first race. If both run at the same pace, Jordan effectively 'catches up' to where he finished ahead in the first race. Hence, they would end the race at the same moment, and since Jordan has to run 23 meters more, it's clear he's still the faster runner.

Answer 2

Jordan wins the second race.

Step-by-step explanation:

Jordan and Amari run a 200-meter race, and Jordan wins by 23 meters.

This means that while Jordan ran 200 meters, Amari will have ran 200 - 23 = 177 meters.

Thus, for each meter that Jordan runs, Amari runs 177/200 = 0.885 meters.

Second race:

Jordan starting 23 meters behind the starting line, and thus, he will have to run 200 + 23 = 223 meters.

When Jordan reaches the finish line, having ran 223 meters(200 + 23 behind), Amari will have ran 223*0.885 = 197.335 meters(< 200, so he will not have reached the finish line), and thus, Jordan wins the second race.