Question

Решите пожалуйста задачу по действиям. В 7 час утра из Москвы вышел поезд со скоростью 60 км/ час. В 13 час следующего дня в том же направлении вылетел самолёт со скоростью 660 км/ час. Через сколько часов самолёт догонит поезд.

Answer 1

Problem Analysis

To solve this problem, we need to find the time it takes for the plane to catch up with the train. We can use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

Train's Travel Time

The train travels for 30 hours (from 7 am to 1 pm the next day).

Distance Covered by the Train

\[ \text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 30 \, \text{h} = 1800 \, \text{km} \]

Relative Speed of the Plane

The relative speed of the plane with respect to the train is the difference between the speed of the plane and the speed of the train. \[ \text{Relative Speed} = 660 \, \text{km/h} - 60 \, \text{km/h} = 600 \, \text{km/h} \]

Time Taken for the Plane to Catch Up

\[ \text{Time} = \frac{1800 \, \text{km}}{600 \, \text{km/h}} = 3 \, \text{hours} \]

The plane will catch up with the train in 3 hours.