Questions: Отель предлагает аренду моторной лодки для речной прогулки. Для знакомства с местными достопримечательностями семья Дмитрия решила арендовать моторную лодку. Чтобы успеть к обеду, они должны вернуться обратно в отель не позднее чем через з часа. Дмитрий узнал у администратора отеля, что скорость течения реки составляет 2 км/ч , а собственная скорость лодки не превышает 18 кm/ 4. На какое наибольшее расстояние может отплыть семья от отеля на моторной лодке? В ответе укажите целое число километров.

Отель предлагает аренду моторной лодки для речной прогулки. Для знакомства с местными достопримечательностями семья Дмитрия решила арендовать моторную лодку. Чтобы успеть к обеду, они должны вернуться обратно в отель не позднее чем через з часа. Дмитрий узнал у администратора отеля, что скорость течения реки составляет 2 км/ч , а собственная скорость лодки не превышает 18 кm/ 4. На какое наибольшее расстояние может отплыть семья от отеля на моторной лодке? В ответе укажите целое число километров.
Transcript text: Отель предлагает аренду моторной лодки для речной прогулки. Для знакомства с местными достопримечательностями семья Дмитрия решила арендовать моторную лодку. Чтобы успеть к обеду, они должны вернуться обратно в отель не позднее чем через з часа. Дмитрий узнал у администратора отеля, что скорость течения реки составляет 2 км/ч , а собственная скорость лодки не превышает 18 кm/ 4. На какое наибольшее расстояние может отплыть семья от отеля на моторной лодке? В ответе укажите целое число километров.
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Solution

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Solution Steps

Step 1: Understand the Problem

The family wants to rent a motorboat to explore the river and return to the hotel within 3 hours. The river's current speed is 2 km/h, and the boat's own speed is 18 km/h. We need to find the maximum distance they can travel from the hotel and return within the given time.

Step 2: Determine Effective Speeds

The effective speed of the boat when going downstream (with the current) is the sum of the boat's speed and the current speed: \[ v_{\text{downstream}} = 18 + 2 = 20 \text{ km/h} \] The effective speed of the boat when going upstream (against the current) is the difference between the boat's speed and the current speed: \[ v_{\text{upstream}} = 18 - 2 = 16 \text{ km/h} \]

Step 3: Calculate Maximum Distance

Let \( d \) be the maximum distance the family can travel from the hotel. The time taken to travel downstream and upstream must sum to 3 hours: \[ \frac{d}{20} + \frac{d}{16} = 3 \]

Step 4: Solve the Equation

To solve for \( d \), find a common denominator and solve the equation: \[ \frac{d}{20} + \frac{d}{16} = 3 \] \[ \frac{4d + 5d}{80} = 3 \] \[ \frac{9d}{80} = 3 \] \[ 9d = 240 \] \[ d = \frac{240}{9} \approx 26.6667 \]

Step 5: Round to the Nearest Whole Number

Since the problem asks for the maximum distance in whole kilometers, round down to the nearest whole number: \[ d = 26 \]

Final Answer

The maximum distance the family can travel from the hotel is \(\boxed{26}\) kilometers.

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