Question

Два поезда выехали с одной станции в одном направлении. первый поезд выехал на 2 ч раньше другого и движется со скоростью 40 км/ч второй поезд со скорость 80 км/ч. через сколько часов второй поезд догонит первый? на каком расстоянии от станции отправления второй поезд догонит первый?

Answer 1

К моменту выхода второго поезда первый проедет 40*2 = 80 км.
Скорость сближения 80-40 = 40 км/ч.
Первый догонит второго через 80:40 = 2 часа после своего выхода.
Расстояние от станции будет 2*80 = 160 км.

Answer 2

Problem Analysis

We have two trains that depart from the same station in the same direction. The first train departs 2 hours earlier than the second train and travels at a speed of 40 km/h, while the second train travels at a speed of 80 km/h. We need to determine how many hours it will take for the second train to catch up to the first train and at what distance from the departure station this will occur.

Solution

Let's assume that the time it takes for the second train to catch up to the first train is t hours. During this time, the first train will have traveled for t + 2 hours, and the second train will have traveled for t hours.

To find the distance at which the second train catches up to the first train, we can set up the following equation:

Distance traveled by the first train = Distance traveled by the second train

Since distance = speed × time, we can write:

40 × (t + 2) = 80 × t

Simplifying the equation:

40t + 80 = 80t

80 = 80t - 40t

80 = 40t

t = 2

Therefore, it will take the second train 2 hours to catch up to the first train. To find the distance at which this occurs, we can substitute the value of t into the equation:

Distance = speed × time

Distance = 80 × 2

Distance = 160 km

Answer

The second train will catch up to the first train after 2 hours. At that time, the second train will be 160 km away from the departure station.