Question

Колонна войск, растянувшись в длину на2 км, движется по шоссе со скоростью5 км/ч. Командир, находясь в "хвосте" колонны, посылает мотоциклиста с донесением головному отряду. Через 11 мин мотоциклист возвратился. Какова скорость мотоциклиста, если на передачу донесения он потратил 1 мин? Считать, что скорость мотоциклиста в обоих направлениях одинакова.

Answer 1

L=2 км 

Vk=5 км/ч 

t=11 мин = 11/60 ч

t1= 1 мин =1/60 ч

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Vм -?

 

РЕШЕНИЕ

 

СПОСОБ 1  (Через 11 мин мотоциклист возвратился.)

скорости постоянные

вперед мотоциклист проехал L= 2 км со скоростью (Vм- Vk)

за время t1=L/(Vм- Vk) ч

назад мотоциклист проехал L= 2 км со скоростью (Vм+Vk)

за время t2=L/(Vм+ Vk) ч

составим уравнение по времени

t=t1+t2

t=L/(Vм- Vk) +L/(Vм+ Vk)=L*2Vм/(Vм^2- Vk^2)

подставим значения

11/60  = 2* 2*Vм / (Vм^2-5^2)

11/60*(Vм^2-5^2) = 4Vм 

11/60*Vм^2 -4*Vм -55/12 = 0

решим квадратное уравнение

x=5/11*(24+√697 )=22.9 км/ч = 23 км/ч

 

Ответ 23 км/ч скорость мотоциклиста

 

СПОСОБ 2  (если на передачу донесения он потратил 1 мин)

скорости постоянные

вперед мотоциклист проехал L= 2 км со скоростью (Vм- Vk)

за время t1=L/(Vм- Vk) ч

подставим значения

1/60  = 2/ (Vм^2-5^2)

(Vм^2-5^2)=120

Vм^2 = 120-25=95

Vм = √95= 9.7 км/ч = 10 км/ч

 

Ответ = 9.7 км/ч = 10 км/ч

Answer 2

Problem Analysis

We are given a scenario where a column of troops, stretched out over a distance of 2 km, is moving along a road at a speed of 5 km/h. The commander, who is at the "tail" of the column, sends a motorcyclist with a message to the main unit. After 11 minutes, the motorcyclist returns. We need to determine the speed of the motorcyclist, assuming that the speed in both directions is the same.

Solution

To solve this problem, we can use the formula: speed = distance / time.

Let's break down the information given in the problem:

- Distance covered by the column of troops: 2 km - Speed of the column of troops: 5 km/h - Time taken by the motorcyclist to deliver the message: 11 minutes - Time taken by the motorcyclist to return: 1 minute

We need to find the speed of the motorcyclist. Since the speed in both directions is the same, we can assume that the time taken to deliver the message is the same as the time taken to return.

Calculation

Let's calculate the speed of the motorcyclist using the formula mentioned earlier:

- Distance covered by the motorcyclist to deliver the message: 2 km - Time taken by the motorcyclist to deliver the message: 11 minutes = 11/60 hours - Speed of the motorcyclist = Distance / Time = 2 km / (11/60) hours

Simplifying the calculation:

- Speed of the motorcyclist = 2 km / (11/60) hours = 2 km * (60/11) / 1 hour = 120/11 km/h

Answer

The speed of the motorcyclist is approximately 10.91 km/h.

Explanation

The motorcyclist traveled a distance of 2 km to deliver the message and then returned the same distance. The total time taken for the round trip was 11 minutes to deliver the message and 1 minute to return. Since the speed in both directions is the same, we can calculate the speed by dividing the total distance traveled (2 km) by the total time taken (12 minutes = 11 minutes + 1 minute). This gives us a speed of approximately 10.91 km/h for the motorcyclist.