Question

Из пункта А выехал автобус,а через 15 минут 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

Х  - скорость 1-го автобуса1,2*х - скорость 2-го автобуса45/х - время в пути 1-го автобуса45/1,2х - время в пути 2-го автобуса Известно, что второй выехал на 15 минут позже:15 минут = 15/60 =  0,25 Составим уравнение:45/х - 45/1,2х = 0,251,2х * 0,25 = 45*1,2 - 450,3х = 9х = 30 Ответ. 30 км/ч скорость первого автобуса.

Answer 2

Calculating the Speed of the First Bus

To find the speed of the first bus, we can use the concept of relative speed. Let's denote the speed of the first bus as x km/h and the speed of the second bus as 1.2x km/h.

Relative Speed and Time Equation

When the second bus catches up to the first bus, the distance covered by the first bus plus the distance covered by the second bus is equal to the distance between them, which is 45 km. We can use the formula:

Distance = Speed × Time

The time taken by the first bus is t hours, and the time taken by the second bus is (t - 15/60) hours (15 minutes is converted to hours).

Setting Up the Equation

Using the relative speed concept, we can set up the equation:

Distance covered by the first bus + Distance covered by the second bus = Total distance

x * t + 1.2x * (t - 15/60) = 45

Solving for the Speed of the First Bus

Solving the equation will give us the value of x, which represents the speed of the first bus.

Let's calculate the speed of the first bus using the given information and the equation mentioned above.