Question

Роз'яжіть задачу по діям: Відстань від Одеси до Роздільної 86,4 км. Одночасно в одному напрямку вирушили велосипедист зі швидкістю 13,5км/год й пішозід - зі швидкісьтю, у 5 разів меншою. Через скільки годин велосипедист наздожине пішехода?

Answer 1

Problem Analysis

To solve this problem, we need to determine the time it takes for the cyclist to catch up with the pedestrian. We are given the distance between Odessa and Rozdilna, the speed of the cyclist, and the speed of the pedestrian.

Solution

Let's break down the problem step by step:

1. Convert the speed of the cyclist from km/h to km/min. Since we will be working with time in minutes, it is easier to have the speed in km/min. To convert km/h to km/min, we divide the speed by 60.

- Speed of the cyclist: 13.5 km/h - Speed of the cyclist in km/min: 13.5 km/h ÷ 60 = 0.225 km/min

2. Determine the speed of the pedestrian. We are told that the speed of the pedestrian is 5 times slower than the cyclist.

- Speed of the cyclist: 0.225 km/min - Speed of the pedestrian: 0.225 km/min ÷ 5 = 0.045 km/min

3. Calculate the time it takes for the cyclist to catch up with the pedestrian. We can use the formula: time = distance ÷ relative speed. The relative speed is the difference between the speeds of the cyclist and the pedestrian.

- Distance between Odessa and Rozdilna: 86.4 km - Relative speed: 0.225 km/min - 0.045 km/min = 0.18 km/min - Time = 86.4 km ÷ 0.18 km/min = 480 min

4. Convert the time from minutes to hours. Since the question asks for the time in hours, we divide the time in minutes by 60.

- Time in minutes: 480 min - Time in hours: 480 min ÷ 60 = 8 hours

Answer

The cyclist will catch up with the pedestrian in 8 hours.