Question

3) Саша и Маша состязаются в беге на 100м. Если они стартуют одновременно, то в тот момент, когда Маша пересекает линию финиша, Саша успевает пробежать только 95м и Маша выигрывает забег с преимуществом в 5м. Чтобы уравнять шансы, Маша стартует на 5м позади стартовой черты. Оба бегут с той же скоростью, что и раньше. Кто выиграет второй забег?​

Answer 1

Маша выиграет второй забег

Answer 2

Problem Analysis

In this problem, Sasha and Masha are competing in a 100-meter race. Initially, when they start at the same time, Masha wins the race with a 5-meter advantage. To equalize their chances, Masha starts 5 meters behind the starting line. Both Sasha and Masha run at the same speed as before. We need to determine who will win the second race.

Solution

To solve this problem, we need to compare the distances covered by Sasha and Masha in the second race. Let's assume that Sasha's speed is S meters per second and Masha's speed is also S meters per second.

In the first race, when they started at the same time, Masha won with a 5-meter advantage. This means that when Masha crossed the finish line, Sasha had only covered 95 meters. Since both Sasha and Masha run at the same speed, we can calculate the time it took for Masha to finish the race.

The time taken by Masha to finish the race is given by the formula: Time = Distance / Speed

In the first race, Masha covered 100 meters, so the time taken by Masha is: Time taken by Masha = 100 meters / S meters per second

Since Sasha covered only 95 meters in the first race, we can calculate the time it took for Sasha to cover that distance: Time taken by Sasha = 95 meters / S meters per second

Now, in the second race, Masha starts 5 meters behind the starting line. This means that Masha has to cover an additional 5 meters compared to Sasha to reach the finish line.

Let's calculate the time it takes for Masha to cover the additional 5 meters: Time taken by Masha to cover the additional 5 meters = 5 meters / S meters per second

Since both Sasha and Masha run at the same speed, the time taken by Sasha to cover the entire 100 meters is the same as the time taken by Masha to cover 105 meters (100 meters + additional 5 meters).

Now, let's compare the times taken by Sasha and Masha in the second race: - Sasha's time = Time taken by Sasha = 95 meters / S meters per second - Masha's time = Time taken by Masha + Time taken by Masha to cover the additional 5 meters = (100 meters / S meters per second) + (5 meters / S meters per second)

To determine who wins the second race, we need to compare their times. If Sasha's time is less than Masha's time, Sasha wins. Otherwise, Masha wins.

Answer

To determine who wins the second race, we need to compare the times taken by Sasha and Masha. If Sasha's time is less than Masha's time, Sasha wins. Otherwise, Masha wins.

Let's calculate their times and compare them: - Sasha's time = 95 meters / S meters per second - Masha's time = (100 meters / S meters per second) + (5 meters / S meters per second)

Since both Sasha and Masha run at the same speed, we can cancel out the common factor of S meters per second in their times. Therefore, we can compare their times without considering the speed.

Comparing their times, we can see that Sasha's time is less than Masha's time. Therefore, Sasha wins the second race.

Example Calculation

Let's assume the speed of both Sasha and Masha is 10 meters per second.

In the first race, Masha won with a 5-meter advantage. Sasha covered only 95 meters, while Masha covered 100 meters. The time taken by Masha to cover 100 meters is: Time taken by Masha = 100 meters / 10 meters per second = 10 seconds

The time taken by Sasha to cover 95 meters is: Time taken by Sasha = 95 meters / 10 meters per second = 9.5 seconds

In the second race, Masha starts 5 meters behind the starting line. Masha has to cover an additional 5 meters compared to Sasha to reach the finish line. The time taken by Masha to cover the additional 5 meters is: Time taken by Masha to cover the additional 5 meters = 5 meters / 10 meters per second = 0.5 seconds

Comparing their times, we can see that Sasha's time (9.5 seconds) is less than Masha's time (10 seconds). Therefore, Sasha wins the second race.

Conclusion

In the second race, Sasha will win the race.