Question

Велосипедист выехал с постоянной скоростью из города А в город В, расстояние между которыми равно 112 км. Отдохнув, он отправился обратно в А, увеличив скорость на 9 км/ч. По пути он сделал остановку на 4 часа, в результате чего затратил на обратный путь столько же времени, сколько на путь из А в В. Найдите скорость велосипедиста на пути из А в В.

Answer 1

Пусть х - это начальная скорость велосипедиста. 112/х - это время, за которое он проехал в одну сторону. (х+9) скорость, когда ехал в обратную сторону. Составляем уравнение:
112/х=112/(х+9)+4
Ответ: 12км/ч.

Answer 2

Problem Analysis

A cyclist travels from city A to city B at a constant speed. After resting, the cyclist returns from city B to city A, increasing their speed by 9 km/h. During the return journey, the cyclist makes a 4-hour stop, which results in the same amount of time spent on the return journey as on the journey from A to B. We need to find the cyclist's speed on the journey from A to B.

Solution

Let's assume the cyclist's speed on the journey from A to B is x km/h.

We know that the distance between city A and city B is 112 km.

The time taken for the journey from A to B can be calculated using the formula: time = distance / speed.

Therefore, the time taken for the journey from A to B is 112 / x hours.

On the return journey, the cyclist increases their speed by 9 km/h, so the speed is now x + 9 km/h.

The time taken for the return journey is the same as the time taken for the journey from A to B, plus the 4-hour stop.

Therefore, the time taken for the return journey is 112 / (x + 9) + 4 hours.

Since the time taken for the return journey is the same as the time taken for the journey from A to B, we can set up the following equation:

112 / x = 112 / (x + 9) + 4

To solve this equation, we can cross-multiply and simplify:

112(x + 9) = 112x + 4(x + 9)

Simplifying further:

112x + 1008 = 112x + 4x + 36

The 112x terms cancel out, and we are left with:

1008 = 4x + 36

Subtracting 36 from both sides:

972 = 4x

Dividing both sides by 4:

x = 243

Therefore, the cyclist's speed on the journey from A to B is 243 km/h.

Answer

The cyclist's speed on the journey from city A to city B is 243 km/h.