Question

Два поезда выходят одновременно из пунктов М и N, расстояние между которыми 45 км, и встречаются через 20 мин. Поезд вышедший из М, прибывает на станцию N на 9 мин раньше, чем другой поезд в М. Какова скорость каждого поезда?

Answer 1

расстояние S =45 км

время до встречи t=20 мин =1/3 час

обозначим скорость 

х - первый из  М

y - второй из  N

тогда встречная скорость   x+y =S/ t  ; x+y = 45 / 1/3 = 135 (1)

время движения первого от M до N

t1 =S / x

время движения второго от N до M

t2 =S / y

по условию  t2 - t1 = 9 мин = 9/60 =3/20 час

S / y - S / x = 3/20  ;   S (1/x -1/y) =3/20 ; 45 (1/x -1/y) =3/20 ;  (1/x -1/y) = 1/300   (2)

решаем сиcтему из (1) (2)

x+y =135  ;                    x = 135 - y

(1/x -1/y) = 1/300 ;       (1/(135-y) -1/y) = 1/300

300 (y -(135-y)) =y *(135-y)

квадратное уравнение

y^2 +465y -40500 =0

y1 = - 540  - отрицательное значение не подходит

y2 = 75 ; тогда  x =135 - 75 = 60

 

ответ

скорость первого  60 км/ч

скорость второго  75  км/ч

Answer 2

Problem Analysis

We have two trains, one starting from point M and the other starting from point N. The distance between M and N is 45 km. The trains meet after 20 minutes. The train that started from M arrives at station N 9 minutes earlier than the other train arrives at M. We need to find the speed of each train.

Solution

Let's assume the speed of the train starting from M is v1 and the speed of the train starting from N is v2.

To find the speed of each train, we can use the formula:

Speed = Distance / Time

We know that the distance between M and N is 45 km. Let's calculate the time it takes for the trains to meet.

The train starting from M travels for 20 minutes, and the train starting from N also travels for 20 minutes. Therefore, the total time taken for the trains to meet is 20 minutes.

Now, let's calculate the time it takes for the train starting from M to reach station N and the time it takes for the other train to reach M.

The train starting from M arrives at station N 9 minutes earlier than the other train arrives at M. Therefore, the time taken for the train starting from M to reach station N is 20 minutes - 9 minutes = 11 minutes.

Now, we can calculate the speed of each train using the formula mentioned earlier.

Speed of train starting from M (v1) = Distance / Time = 45 km / 11 minutes

Speed of train starting from N (v2) = Distance / Time = 45 km / 20 minutes

Let's calculate the speeds:

Speed of train starting from M (v1) = 45 km / 11 minutes = 4.09 km/minute

Speed of train starting from N (v2) = 45 km / 20 minutes = 2.25 km/minute

Therefore, the speed of the train starting from M is approximately 4.09 km/minute and the speed of the train starting from N is approximately 2.25 km/minute.