Question

Вопрос: Команда из Ержана, Алихана и одноместного самоката участвует гонке. Дистанция разделена на участки одинаковой длины, их количество равно 42, в начале каждого - контрольный пункт. Ержан пробегает участок за 9 минут, Алихан - за 11 минут, а на самокате любой из них проезжает участок за 3 минуты. Стартуют они одновременно, а на финише учитывается время того, кто пришел последним. Ребята договорились, что один проезжает первую часть пути на самокате, остаток бегом, а другой - наоборот (самокат можно оставить на любом контрольном пункте). Сколько участков Ержан должен проехать на самокате, чтобы команда показала наилучшее время? Варианты: A 9 B 14 C 15 D 18 E 25​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To find the answer to this question, we need to determine the optimal strategy for Erzhan and Alihan to achieve the best time in the race. Let's break down the information given:

- The race consists of 42 equal-length segments, each with a checkpoint at the beginning. - Erzhan completes each segment in 9 minutes. - Alihan completes each segment in 11 minutes. - Either Erzhan or Alihan can complete each segment on a scooter in 3 minutes. - They start the race simultaneously, and the finishing time is based on the time of the last person to arrive.

To find the best strategy, we need to consider the time it takes for each person to complete the segments. Let's analyze the options:

1. Erzhan completes the first part on the scooter and the remaining part on foot, while Alihan does the opposite. - In this case, Erzhan would spend 3 minutes per segment for the first part and 9 minutes per segment for the remaining part. Alihan would spend 11 minutes per segment for the first part and 3 minutes per segment for the remaining part. - The total time for Erzhan would be 3 * x + 9 * (42 - x), where x is the number of segments Erzhan completes on the scooter. - The total time for Alihan would be 11 * (42 - x) + 3 * x. - To find the best time, we need to minimize the total time for both Erzhan and Alihan.

Let's calculate the total time for each option:

- Option A: Erzhan completes 9 segments on the scooter (x = 9). - Erzhan's total time: 3 * 9 + 9 * (42 - 9) = 27 + 279 = 306 minutes. - Alihan's total time: 11 * (42 - 9) + 3 * 9 = 33 * 33 + 27 = 1089 minutes.

- Option B: Erzhan completes 14 segments on the scooter (x = 14). - Erzhan's total time: 3 * 14 + 9 * (42 - 14) = 42 + 252 = 294 minutes. - Alihan's total time: 11 * (42 - 14) + 3 * 14 = 28 * 33 + 42 = 924 minutes.

- Option C: Erzhan completes 15 segments on the scooter (x = 15). - Erzhan's total time: 3 * 15 + 9 * (42 - 15) = 45 + 243 = 288 minutes. - Alihan's total time: 11 * (42 - 15) + 3 * 15 = 27 * 33 + 45 = 891 minutes.

- Option D: Erzhan completes 18 segments on the scooter (x = 18). - Erzhan's total time: 3 * 18 + 9 * (42 - 18) = 54 + 216 = 270 minutes. - Alihan's total time: 11 * (42 - 18) + 3 * 18 = 24 * 33 + 54 = 846 minutes.

- Option E: Erzhan completes 25 segments on the scooter (x = 25). - Erzhan's total time: 3 * 25 + 9 * (42 - 25) = 75 + 153 = 228 minutes. - Alihan's total time: 11 * (42 - 25) + 3 * 25 = 17 * 33 + 75 = 636 minutes.

Based on the calculations, the option that gives the best time for the team is Option E: Erzhan should complete 25 segments on the scooter.

Please note that the time calculations are based on the given information and assumptions made.