Question

Из пункта А выехал автобус , а через 15 мин в том же направлении выехал другой автобус со скоростью в 1.2 раза большей и догнал первый на расстоянии 45 км от А .Найдите скорость первого автобуса

Answer 1

Пускай х км/ч скорость первого автобуса, тогда 1,2х км/ч - скорость второго автобуса. Расстояние автобусы проехали 45 км, составляем уравнение по времени в пути каждого из них (15 мин=0,25 ч): 45/х-45/1,2х=0,25. Приводим к общему знаменателю, отмечаем, что х не 0, отбросим его и получаем: 45*1,2-45=0,25*1,2х, 54-45=0,3х, 9=0,3х, 90=3х, х=30 км/ч скорость первого автобуса.

Answer 2

Problem Analysis

We are given that a bus departs from point A, and after 15 minutes, another bus departs from the same point A in the same direction. The second bus has a speed that is 1.2 times greater than the speed of the first bus. The second bus catches up to the first bus at a distance of 45 km from point A. We need to find the speed of the first bus.

Solution

Let's assume the speed of the first bus is x km/h. Since the second bus has a speed that is 1.2 times greater, its speed is 1.2x km/h.

We know that the time taken by both buses to reach the catching point is the same. Let's calculate the time taken by each bus.

The time taken by the first bus is 15 minutes, which is equal to 15/60 = 0.25 hours.

The time taken by the second bus is the same as the first bus because they both reach the catching point at the same time.

We can use the formula speed = distance/time to calculate the speed of each bus.

For the first bus: x = 45/0.25 km/h

For the second bus: 1.2x = 45/0.25 km/h

Now, let's solve these equations to find the value of x.

Calculation

Using the equation x = 45/0.25, we can calculate the speed of the first bus.

x = 45/0.25 = 180 km/h

Therefore, the speed of the first bus is 180 km/h.

Answer

The speed of the first bus is 180 km/h.

Explanation

The first bus has a speed of 180 km/h, and the second bus has a speed of 1.2 times that, which is 216 km/h. Both buses take the same amount of time to reach the catching point, which is 45 km from point A.