Question

Из двух городов одновременно навстречу друг другу отправились два велосипедиста. Проехав некоторую часть пути, первый велосипедист сделал остановку на 36 минут, а затем продолжил движение до встречи со вторым велосипедистом. Расстояние между городами составляет 120 км, скорость первого велосипедиста равна 10 км/ч, скорость второго - 20 км/ч. Определите расстояние от города, из которого выехал второй велосипедист, до места встречи.

Answer 1

36 мин = 36/60 = 6/10 = 3/5
1 ехал t часов
Проехал 10t км.
2 ехал t+3/5 часа
Проехал 20(t+3/5) = 20t+12 км
10t+20t+12=120
30t=120-12
30t=108
t=3,6
1 проехал 10t = 10*3,6 = 36 км.
2 проехал 120-36 = 84 км.
Ответ: 84 км

Answer 2

Problem Analysis

We have two cyclists who start simultaneously from two different cities and meet each other after one of them takes a 36-minute break. The distance between the cities is 120 km, and the first cyclist's speed is 10 km/h, while the second cyclist's speed is 20 km/h. We need to determine the distance from the city where the second cyclist started to the meeting point.

Solution

Let's denote the distance from the city where the second cyclist started to the meeting point as x km.

The first cyclist traveled for some time, then took a 36-minute break, and then continued until reaching the meeting point. The second cyclist traveled the entire distance without any breaks.

To find the distance x, we can set up an equation based on the time and distance traveled by each cyclist.

The time it took for the first cyclist to reach the meeting point can be calculated as follows: - The distance traveled by the first cyclist before the break is 120 - x km. - The time taken by the first cyclist before the break is (120 - x) / 10 hours. - The time taken by the first cyclist after the break is (120 - x) / 10 + 36/60 hours.

The time it took for the second cyclist to reach the meeting point is: - The distance traveled by the second cyclist is x km. - The time taken by the second cyclist is x / 20 hours.

Since both cyclists started at the same time, their total travel times should be equal. Therefore, we can set up the following equation:

(120 - x) / 10 + 36/60 = x / 20

Now, let's solve this equation to find the value of x.

Calculation

(120 - x) / 10 + 36/60 = x / 20

To simplify the equation, let's convert 36 minutes to hours: 36 minutes = 36/60 hours = 0.6 hours

(120 - x) / 10 + 0.6 = x / 20

Multiply both sides of the equation by 20 to eliminate the denominators: 2(120 - x) + 12 = x

240 - 2x + 12 = x

252 = 3x

x = 252 / 3

x = 84

Answer

The distance from the city where the second cyclist started to the meeting point is 84 km.

Explanation

The first cyclist traveled 120 - 84 = 36 km before taking a break. After the break, the first cyclist traveled an additional 36/60 = 0.6 hours at a speed of 10 km/h, which is 0.6 * 10 = 6 km. Therefore, the total distance traveled by the first cyclist is 36 + 6 = 42 km.

The second cyclist traveled the entire distance of 84 km without any breaks.

The total distance traveled by both cyclists is 42 + 84 = 126 km, which is equal to the distance between the two cities.

Therefore, the solution is consistent with the given information.

Verification

Let's verify the solution using the given information.

The first cyclist traveled 42 km at a speed of 10 km/h, which took 42 / 10 = 4.2 hours.

The second cyclist traveled 84 km at a speed of 20 km/h, which took 84 / 20 = 4.2 hours.

Both cyclists took the same amount of time to reach the meeting point, which confirms the solution.