Question

Из пункта А по одному и тому же маршруту одновременно выехали грузовик и легковой автомобиль. Скорость легкового автомобиля постоянна и составляет 6/5 скорости грузовика. Через 30 минут за ними из того же пункта выехал мотоциклист со скоростью 90 км/ч. Найдите скорость легкового автомобиля, если известно, что мотоциклист догнал грузовик на час раньше, чем легковой автомобиль.

Answer 1

Пусть скорость грузовика х, тогда легкового автомобиля 1,2*х.
Рассмотрим путь мотоциклиста до встречи с грузовым и легковым автомобилями.
90*t-45=t*x    90*t-t*x=45   t*(90-x)=45 t=45/90-x, подставим
90*(t+1)-45=(t+1)*1,2*x
90*t+90-45=1,2*x*t+1,2*x
90*t+45=1,2*x*t+1/2*x
(90*45)/(90-x)+45=(1,2*x*45)/(90-x)+1,2*x
90*45+45*(90-x)=1,2*x*45+1,2*x*(90-x)
90*45+90*45-45*x=54*x+108*x-1,2*x^2
1,2*x^2-207*x+8100=0
x1,2=(207±√207^2-4*1,2*8100)/2,4=(207±63)/2,4
x1=(207+63)/2,4=112,5 не подходит, мотоцикл ехал со скоростью 90, не смог бы догнать.
x2=(207-63)/2,4=60 км/ч скорость грузовика
60*1,2=72 км/ч скорость легкового автомобиля.

Answer 2

Problem Analysis

We are given that a truck and a car start simultaneously from point A and travel on the same route. The car's speed is constant and is 6/5 times the speed of the truck. After 30 minutes, a motorcyclist starts from the same point A and catches up with the truck one hour before catching up with the car. We need to find the speed of the car.

Solution

Let's assume the speed of the truck is x km/h. Therefore, the speed of the car is (6/5)x km/h.

We know that the motorcyclist catches up with the truck one hour before catching up with the car. This means that the time taken by the motorcyclist to catch up with the truck is one hour less than the time taken to catch up with the car.

Let's calculate the time taken by the motorcyclist to catch up with the truck and the car.

The time taken by the motorcyclist to catch up with the truck can be calculated using the formula:

time = distance / speed

The distance covered by the motorcyclist in catching up with the truck is the same as the distance covered by the truck in the same time. Therefore:

distance covered by truck = speed of truck * time

Similarly, the distance covered by the motorcyclist in catching up with the car is the same as the distance covered by the car in the same time. Therefore:

distance covered by car = speed of car * (time + 1 hour)

Since the distances covered by the motorcyclist in catching up with the truck and the car are the same, we can equate the two equations:

speed of truck * time = speed of car * (time + 1 hour)

Simplifying the equation:

x * time = (6/5)x * (time + 1 hour)

Solving for time:

time = (6/5)x * (time + 1 hour) / x

Simplifying further:

time = (6/5) * (time + 1 hour)

Expanding the equation:

5 * time = 6 * (time + 1 hour)

Simplifying:

5 * time = 6 * time + 6

time = 6

Therefore, the time taken by the motorcyclist to catch up with the truck is 6 hours.

Now, we can calculate the speed of the car using the time taken by the motorcyclist to catch up with the car:

speed of car = distance covered by car / (time + 1 hour)

Substituting the values:

speed of car = (6/5)x * (6 + 1 hour) / (6 + 1 hour)

Simplifying:

speed of car = (6/5)x

Therefore, the speed of the car is (6/5)x km/h.

Answer

The speed of the car is (6/5)x km/h, where x is the speed of the truck.

Note: The specific value of the speed of the car cannot be determined without knowing the speed of the truck.