Question

Пассажирский поезд едет вслед за товарным. В 6 часов утра расстояние между ними было 70 км. Скорость пассажирского поезда 80км/ч, а скорость товарного 60км/ч. Успеет ли пассажирский поезд догнать товарный до 9 часов утра? Через сколько времени произойдет встреча?

Answer 1

С 6-00 до 9-00 пройдет 9-6=3 часа;
скорость сближения - 80-60=20 км/час;
20*3=60 км - на столько приблизится пассажирский поезд к товарному;
70-60=10 км останется между ними в 9-00;
70/20=3,5 часа, 3 часа 30 минут;
Ответ: нет, не сможет, время до встречи 3 часа 30 минут.

Answer 2

Given Information

The passenger train is traveling at a speed of 80 km/h, and the freight train is traveling at a speed of 60 km/h. At 6:00 AM, the distance between them was 70 km.

Time to Overtake

To determine if the passenger train will catch up to the freight train by 9:00 AM, we can calculate the distance covered by each train during this time.

The passenger train's position at 6:00 AM can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] \[ \text{Distance}_{\text{passenger}} = 80 \, \text{km/h} \times 3 \, \text{h} = 240 \, \text{km} \]

The freight train's position at 6:00 AM can be calculated using the same formula: \[ \text{Distance}_{\text{freight}} = 60 \, \text{km/h} \times 3 \, \text{h} = 180 \, \text{km} \]

The distance between the trains at 6:00 AM is \( 240 \, \text{km} - 180 \, \text{km} = 60 \, \text{km} \).

Given that the passenger train is 60 km ahead at 6:00 AM, it will overtake the freight train at some point after that.

Time of Overtaking

To find out when the overtaking will occur, we can use the relative speed of the passenger train with respect to the freight train, which is \( 80 \, \text{km/h} - 60 \, \text{km/h} = 20 \, \text{km/h} \).

The time it takes for the passenger train to overtake the freight train can be calculated using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \] \[ \text{Time} = \frac{60 \, \text{km}}{20 \, \text{km/h}} = 3 \, \text{h} \]

Therefore, the passenger train will overtake the freight train 3 hours after 6:00 AM, which is at 9:00 AM.

Conclusion

The passenger train will indeed overtake the freight train by 9:00 AM, which is 3 hours after 6:00 AM.