Question

Из пункта А а в пункт В выехал автомобиль , через 45 мин из пункта А в пункт В выехал мотоцикл, со сокростью на 20 км./ч больше автомобиля. На расстоянии 180 км. от пункта а они встретились. Надо найти скорость автомобиля и скорость мотоцикла

Answer 1

Пусть:
х - скорость автомобиля. 
у - скорость мотоцикла. 
"..скорость мотоцикла на 20 км/ч больше скорости автомобиля" -> у=х+20 - первое уравнение 

Время за которое мотоцикл проехал 180 км равно 180/у . .Автомобиль находился в пути на 45 мин(3/4 часа) больше. 
(180/у)-(180/х)=3/4 - второе ур 
подставляем первое по второе: 180/(х+20)-(180/х)-3/4=0 ; избавляемся от знаменателей(умножаем обе части уравнения на ((х+20)*х*4), получаем: 

х*х+х*20-3600=0 
х=50 (второй корень, отрицательный, отбрасываем ) 
у=х+20=50+20=70 

Ответ: скорость автомобиля 50 км/ч, скорость мотоцикла 70 км/ч

Answer 2

Problem Analysis

We are given that a car and a motorcycle traveled from point A to point B. The motorcycle started 45 minutes after the car and had a speed 20 km/h faster than the car. They met each other 180 km away from point A. We need to find the speed of the car and the speed of the motorcycle.

Solution

Let's assume the speed of the car is x km/h. Since the motorcycle is 20 km/h faster, its speed will be x + 20 km/h.

We know that the car traveled for 45 minutes longer than the motorcycle. Since 1 hour is equal to 60 minutes, the car traveled for 45/60 = 0.75 hours longer than the motorcycle.

To find the distance traveled by the car, we can use the formula: distance = speed * time.

The distance traveled by the car is the sum of the distance traveled by the motorcycle and the 180 km where they met. So we have the equation:

x * (t + 0.75) = (x + 20) * t + 180

Simplifying the equation:

xt + 0.75x = xt + 20t + 180

0.75x = 20t + 180

Now, we need to find the value of t in terms of x. To do that, we can use the fact that the distance traveled by the motorcycle is equal to the speed of the motorcycle multiplied by the time it traveled:

x * t = (x + 20) * t

xt = xt + 20t

20t = 0

Since 20t = 0, we can conclude that t = 0.

Substituting t = 0 into the equation 0.75x = 20t + 180, we get:

0.75x = 180

Solving for x:

x = 180 / 0.75

x = 240

Therefore, the speed of the car is 240 km/h.

Since the motorcycle is 20 km/h faster, its speed is 240 + 20 = 260 km/h.

Answer

The speed of the car is 240 km/h and the speed of the motorcycle is 260 km/h.