Question

Расстояние 160км автобус преодолел за время на 2 ч больше,чем автомобиль.С какой скоростью он двигался,если его скорость была в 2 раза меньше,чем у автомобиля.

Answer 1

V -скорость автобуса

2V - скорость автомобиля

160/V - 2 = 160/2V

Приведем к общему знаменателю 2V, получим

320-4V=160

4V=160

V=40 (км/ч) - скорость автобуса

Answer 2

Problem Analysis

We are given that a bus traveled a distance of 160 km in a time that was 2 hours longer than the time it took for a car to travel the same distance. The speed of the bus was also stated to be half the speed of the car. We need to determine the speed at which the bus was traveling.

Solution

Let's assume the speed of the car is x km/h. Since the speed of the bus is half that of the car, the speed of the bus is x/2 km/h.

We can use the formula speed = distance / time to calculate the time it took for the car and the bus to travel the distance of 160 km.

For the car: x = 160 / t, where t is the time taken by the car.

For the bus: (x/2) = 160 / (t + 2), where t + 2 is the time taken by the bus (2 hours longer than the car).

To solve this system of equations, we can substitute the value of x from the first equation into the second equation and solve for t.

Let's solve the equations to find the value of t and then calculate the speed of the bus.

Calculation

From the first equation, we have x = 160 / t.

Substituting x = 160 / t into the second equation, we get (160 / (2t)) = 160 / (t + 2).

Simplifying the equation, we have 160(t + 2) = 2t * 160.

Expanding and simplifying further, we get 160t + 320 = 320t.

Bringing the terms with t to one side, we have 320t - 160t = 320.

Simplifying, we get 160t = 320.

Dividing both sides by 160, we find t = 2.

Now that we have the value of t, we can substitute it back into the first equation to find the speed of the car.

From the first equation, we have x = 160 / t.

Substituting t = 2, we get x = 160 / 2.

Simplifying, we find x = 80.

Therefore, the speed of the car is 80 km/h.

Since the speed of the bus is half that of the car, the speed of the bus is 80 / 2 = 40 km/h.

Answer

The bus was traveling at a speed of 40 km/h.