Question

Путешественник 3 часа ехал на автобусе и 4 часа на поезде, преодолев за это время путь 465 км. Найдите скорость автобуса, если она на 55 км/ч меньше скорости поезда

Answer 1

Пусть х скорость автобуса
тогда х+55 - скорость поезда
3х+4(х+55)=465
3х+4х+220=465
7х=245
х=35 -скорость автобуса
90- скорость поезда

Answer 2

Problem Analysis

A traveler spends 3 hours on a bus and 4 hours on a train, covering a total distance of 465 km. We need to find the speed of the bus, given that it is 55 km/h slower than the speed of the train.

Solution

Let's assume the speed of the train is x km/h. According to the problem, the speed of the bus is 55 km/h slower than the speed of the train, so the speed of the bus can be represented as (x - 55) km/h.

We know that speed is equal to distance divided by time. We can use this formula to find the speed of the train and the bus.

The distance covered by the bus is equal to the product of its speed and the time it traveled, which is 3 hours. Similarly, the distance covered by the train is equal to the product of its speed and the time it traveled, which is 4 hours. The sum of these distances should be equal to the total distance of 465 km.

Let's set up the equation:

(x - 55) * 3 + x * 4 = 465

Now, let's solve this equation to find the value of x, which represents the speed of the train.

Calculation

(x - 55) * 3 + x * 4 = 465

Expanding the equation:

3x - 165 + 4x = 465

Combining like terms:

7x - 165 = 465

Adding 165 to both sides:

7x = 630

Dividing both sides by 7:

x = 90

The speed of the train, x, is 90 km/h.

Now, we can find the speed of the bus by subtracting 55 km/h from the speed of the train:

Speed of the bus = Speed of the train - 55 = 90 - 55 = 35 km/h

Answer

The speed of the bus is 35 km/h.