Question

От одной автостанции по одному и тому же маршруту с интервалом в 1час отправились сначала автобус, затем легковые такси. Средняя скорость автобуса -60км/ч,а такси-80км/ч. Через сколько часов такси догонит автобус?

Answer 1

Решаем таблицей
такси автобус
1час 0 60
2 80 120
3 160 180
4 240 240
следовательно встретятся через 4 часа

Answer 2

Problem Analysis

We are given that a bus and a taxi start from the same bus station, following the same route, with a 1-hour interval between their departures. The average speed of the bus is 60 km/h, and the average speed of the taxi is 80 km/h. We need to determine how many hours it will take for the taxi to catch up to the bus.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed is the difference between the speeds of two objects moving in the same direction.

Let's assume that the taxi catches up to the bus after t hours. During this time, the bus would have traveled a distance of 60t km, and the taxi would have traveled a distance of 80t km.

Since the taxi catches up to the bus, the distance traveled by the taxi must be equal to the distance traveled by the bus. Therefore, we can set up the following equation:

80t = 60t

Simplifying the equation, we get:

20t = 0

Since the equation has no solution, it means that the taxi will never catch up to the bus. This is because the taxi is faster than the bus, and with a 1-hour interval between their departures, the taxi will always be ahead of the bus.

Answer

The taxi will never catch up to the bus.

Explanation

The average speed of the taxi is 80 km/h, while the average speed of the bus is 60 km/h. Since the taxi is faster than the bus, it will always be ahead of the bus. With a 1-hour interval between their departures, the taxi will continue to maintain its lead and will never catch up to the bus.

Conclusion

In this scenario, the taxi will never catch up to the bus because it is faster and has a head start.