Question

Из двух городов расстояние между которыми 480 км одновременно в одном направлении выехал поезд и вылетел самолет. самолет догнал поезд через 40 мин после вылета. С какой скоростью двигались поезд и самолет, если скорость поезда была в 9 раз меньше скорости самолета?

Answer 1

40 минут= 2/3 часа

х - скорость поезда
9х - скорость самолета

в пути они были 2/3 часа

путь=скорость*время
поезд прошел  х*2/3
самолет пролетел 9х*2/3
при этом известно, что самолет пролетел на 480 км больше.

2/3х+480=2/3*9х
2/3х+480=6х
5 1/3х=480
16/3х=480
х=480*3/16 
х=90 км/ч скорость поезда
9х=810 км/ч

Answer 2

Скорость поезда х км/час, самолета 9х км/час
за 40 мин пезд прошел расстояние 2/3х, самолет 6х км
6х-2/3х=480
из Уравнения скорость поезда 90 самолета 810

Answer 3

Problem Analysis

We are given that the distance between two cities is 480 km. A train and a plane simultaneously depart from one city in the same direction. The plane catches up to the train 40 minutes after takeoff. We need to determine the speeds of the train and the plane, given that the train's speed is 9 times slower than the plane's speed.

Solution

Let's assume the speed of the train is x km/h and the speed of the plane is y km/h.

We know that the plane catches up to the train 40 minutes (or 2/3 hours) after takeoff. During this time, the plane covers the same distance as the train.

The distance covered by the train in 2/3 hours is (2/3) * x km.

The distance covered by the plane in 2/3 hours is (2/3) * y km.

Since the distance covered by both the train and the plane is the same (480 km), we can set up the following equation:

(2/3) * x = (2/3) * y = 480

Simplifying the equation, we get:

x = y = 480 * (3/2)

Therefore, the speed of the train is 320 km/h and the speed of the plane is 320 km/h.

Answer

The train and the plane both traveled at a speed of 320 km/h.

Explanation

The train and the plane were traveling in the same direction, and the plane caught up to the train 40 minutes after takeoff. Since the train's speed is 9 times slower than the plane's speed, the speeds of both the train and the plane are equal to 320 km/h