Question

Из города А в город Б со скоростью 18 км/ч выехал велосипедист. Через 20 минут в том же направлении выехал мотоциклист со скоростью 30 км/ч. Мотоциклист доехал до Б, повернул обратно и встретил велосипедиста через 30 минут после того, как он обогнал велосипедиста. Чему равно расстояние от А до Б в километрах?

Answer 1

20 мин=1/3ч
30 мин=0,5ч
1/3*18=6 км проехал велосипедист до выезда мотоциклиста
30-18=12 км/ч скорость сближения
6:12=0,5ч через столько мотоциклист обогнал велосипедиста
0,5+0,5=1ч был в пути мотоциклист
1+1/3=4/3 ч был в пути велосипедист
4/3*18=24 км проехал велосипедист до встречи
1*30=30 км всего проехал мотоциклист
(30-24):2=3 км от места встречи до Б
30+3=33 км от А до Б
ответ: 33 км

Answer 2

Problem Analysis

We are given the following information: - A cyclist travels from city A to city B at a speed of 18 km/h. - After 20 minutes, a motorcyclist starts from city A in the same direction as the cyclist, with a speed of 30 km/h. - The motorcyclist reaches city B, turns back, and meets the cyclist 30 minutes after overtaking them.

We need to find the distance between city A and city B.

Solution

Let's break down the problem step by step:

1. Convert the time given in minutes to hours: - 20 minutes = 20/60 = 1/3 hour - 30 minutes = 30/60 = 1/2 hour

2. Calculate the distance traveled by the cyclist in 1/3 hour: - Distance = Speed × Time = 18 km/h × 1/3 hour = 6 km

3. Calculate the distance traveled by the motorcyclist in 1/2 hour: - Distance = Speed × Time = 30 km/h × 1/2 hour = 15 km

4. Let's assume the distance between city A and city B is x km.

5. When the motorcyclist reaches city B, they have traveled x km. They then turn back and meet the cyclist after 30 minutes. At this point, the motorcyclist has traveled a total distance of 2x km.

6. The cyclist has traveled 6 km during this time. Therefore, the distance between the motorcyclist and the cyclist when they meet is 2x - 6 km.

7. Since the motorcyclist is traveling at a faster speed, they cover this distance in less time. The time taken by the motorcyclist to cover this distance is 30 minutes.

8. We can now set up the following equation: - Distance = Speed × Time - (2x - 6) km = 30 km/h × 1/2 hour

9. Solve the equation to find the value of x: - 2x - 6 = 30/2 - 2x - 6 = 15 - 2x = 15 + 6 - 2x = 21 - x = 21/2 - x = 10.5 km

Answer

The distance between city A and city B is 10.5 kilometers.

Explanation

According to the given information, the cyclist travels from city A to city B at a speed of 18 km/h. After 20 minutes, the motorcyclist starts from city A in the same direction as the cyclist, with a speed of 30 km/h. The motorcyclist reaches city B, turns back, and meets the cyclist 30 minutes after overtaking them.

To find the distance between city A and city B, we can use the information provided and solve the problem step by step.

First, we convert the given time in minutes to hours. 20 minutes is equal to 1/3 hour, and 30 minutes is equal to 1/2 hour.

Next, we calculate the distance traveled by the cyclist in 1/3 hour using the formula Distance = Speed × Time. The cyclist's speed is 18 km/h, so the distance traveled is 18 km/h × 1/3 hour = 6 km.

Similarly, we calculate the distance traveled by the motorcyclist in 1/2 hour using the same formula. The motorcyclist's speed is 30 km/h, so the distance traveled is 30 km/h × 1/2 hour = 15 km.

Now, let's assume the distance between city A and city B is x km.

When the motorcyclist reaches city B, they have traveled x km. They then turn back and meet the cyclist after 30 minutes. At this point, the motorcyclist has traveled a total distance of 2x km.

During this time, the cyclist has traveled 6 km. Therefore, the distance between the motorcyclist and the cyclist when they meet is 2x - 6 km.

Since the motorcyclist is traveling at a faster speed, they cover this distance in less time. The time taken by the motorcyclist to cover this distance is 30 minutes.

Setting up the equation Distance = Speed × Time, we have (2x - 6) km = 30 km/h × 1/2 hour.

Solving the equation, we find that 2x - 6 = 15, which simplifies to 2x = 21 and x = 10.5 km.

Therefore, the distance between city A and city B is 10.5 kilometers.