Question

Расстояние между двумя городами составляет 120 км. Мотоциклист и велосипедист выехали из тех мест одновременно. Скорость мотоцикла на 20 км/ч больше скорости велосипедиста. Они встретились в 30 км от одного из населенных пунктов. 1. Сколько км/ч скорость велосипедиста?2.Через сколько часов они встретились?​

Answer 1

Ответ:

Итак, определимся сначала из какого города в 30 км, логично, что мотоциклист быстрее, следовательно он проезжает больше.

Значит велосипедист проехал 30 км, а мотоциклист 120-30=90 км.

t=S/v (v – скорость, S – расстояние, t – время)

$v _{1} = v _{2} + 20$

$v_{1}$ – скорость мотоциклиста;

$v_{2}$ – скорость велосипедиста;

$t = \frac{S_{1} }{v_{1}}$

$t = \frac{S_{2} }{v_{2}}$

У них одинаковое время, ну потому что они не могли встретиться в разные времена, поэтому приравняем два выражения.

$\frac{90}{v_{1} } = \frac{30}{v_{2}}$

$\frac{90}{v_{2} + 20} = \frac{30}{v_{2}}$

Умножаем крест-накрест.

$30(v_{2} + 20) = 90v_{2} \\ v_{2} + 20 = \frac{90v_{2}}{30} \\ v_{2} + 20 = 3v_{2} \\ 3v_{2} - v_{2} = 20 \\ 2v_{2} = 20 \\ v_{2} = \frac{20}{2} \\ v_{2} = 10$

Скорость велосипедиста 10 км/ч.

$t = \frac{30}{10} = 3$

Они встретились через 3 часа.

Answer 2

Given Information:

- The distance between two cities is 120 km. - A motorcyclist and a cyclist started from the same place simultaneously. - The motorcycle's speed is 20 km/h faster than the cyclist's speed. - They met 30 km away from one of the towns.

1. Speed of the cyclist:

Let's assume the speed of the cyclist is x km/h. Since the motorcycle's speed is 20 km/h faster, the speed of the motorcycle is x + 20 km/h.

2. Time taken to meet:

To find the time taken to meet, we need to calculate the time it takes for each of them to cover the distance to the meeting point.

The cyclist covers a distance of 30 km at a speed of x km/h. Therefore, the time taken by the cyclist to cover 30 km is: Time taken by cyclist = Distance / Speed = 30 km / x km/h = 30/x hours.

The motorcycle covers a distance of 120 km - 30 km = 90 km at a speed of x + 20 km/h. Therefore, the time taken by the motorcycle to cover 90 km is: Time taken by motorcycle = Distance / Speed = 90 km / (x + 20) km/h = 90/(x + 20) hours.

Since they started at the same time, the time taken by both of them to meet is the same. Therefore, we can set up the equation:

30/x = 90/(x + 20).

To solve this equation, we can cross-multiply:

30(x + 20) = 90x.

Expanding and simplifying the equation:

30x + 600 = 90x.

Bringing the terms with x to one side:

60x = 600.

Dividing both sides by 60:

x = 10.

Therefore, the speed of the cyclist is 10 km/h.

To find the time taken to meet, we can substitute the value of x into either of the equations:

Time taken by cyclist = 30/x = 30/10 = 3 hours.

Therefore, the cyclist and the motorcyclist will meet after 3 hours.

Summary:

1. The speed of the cyclist is 10 km/h. 2. The cyclist and the motorcyclist will meet after 3 hours.

Please let me know if there's anything else I can help you with!