Question

В океане расположено три острова A, B и C, причем расстояния от A до B и от B до C — по 50 км, а от A до C — 70 км. Одновременно из A в C отправилась яхта, а из CC в BB — катер, оба со скоростью 10 км/ч. Через два часа яхта села на мель и стала подавать сигнал бедствия. Катер тут же изменил курс, увеличил скорость вдвое и последовал к яхте. С острова B к яхте отправилась спасательная лодка со скоростью 20 км/ч. На сколько минут раньше катер прибудет к яхте, чем лодка?

Answer 1

16 минут, на столько катер прибудет к яхте раньше, чем лодка.

Answer 2

Problem Analysis

In this problem, we are given three islands, A, B, and C, with distances between A and B and between B and C both equal to 50 km, and the distance between A and C equal to 70 km. A yacht starts from A and heads towards C, while a motorboat starts from C and heads towards B. After two hours, the yacht runs aground and sends a distress signal. The motorboat immediately changes course, doubles its speed, and heads towards the yacht. A rescue boat is launched from island B towards the yacht with a speed of 20 km/h. We need to determine how many minutes earlier the motorboat will arrive at the yacht compared to the rescue boat.

Solution

To solve this problem, we need to calculate the time it takes for the motorboat and the rescue boat to reach the yacht. Let's break down the solution into steps:

1. Calculate the time it takes for the yacht to run aground: - The yacht travels at a speed of 10 km/h for 2 hours, so the distance covered is 10 km/h * 2 h = 20 km. - Therefore, the yacht runs aground 20 km away from island A.

2. Calculate the time it takes for the motorboat to reach the yacht: - The motorboat changes course and doubles its speed to 10 km/h * 2 = 20 km/h. - The distance between the motorboat and the yacht is 70 km - 20 km = 50 km. - The motorboat travels at a speed of 20 km/h, so the time it takes to cover 50 km is 50 km / 20 km/h = 2.5 hours. - Converting 2.5 hours to minutes, we get 2.5 h * 60 min/h = 150 min.

3. Calculate the time it takes for the rescue boat to reach the yacht: - The distance between island B and the yacht is 50 km. - The rescue boat travels at a speed of 20 km/h, so the time it takes to cover 50 km is 50 km / 20 km/h = 2.5 hours. - Converting 2.5 hours to minutes, we get 2.5 h * 60 min/h = 150 min.

4. Calculate the time difference between the motorboat and the rescue boat: - The motorboat arrives at the yacht 150 min earlier than the rescue boat.

Therefore, the motorboat will arrive at the yacht 150 minutes earlier than the rescue boat.

Answer: The motorboat will arrive at the yacht 150 minutes earlier than the rescue boat.