Question

От одной автостанции по одному и тому же пути маршруту с интервалом в 1 час отправились сначала автобус затем легковое такси средняя скорость автобуса 60 км в час а такси 80 км в час через сколько часов такси догонит автобус

Answer 1

ответ за 1 час и 20 мин

Answer 2

Problem Analysis

We are given that a bus and a taxi start from the same bus station and travel along the same route with an interval of 1 hour. 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 between the taxi and the bus is the difference between their speeds. In this case, the relative speed is 80 km/h - 60 km/h = 20 km/h.

Since the taxi is trying to catch up to the bus, we can consider the distance between them as a fixed value. Let's assume this distance is D km.

The time it takes for the taxi to catch up to the bus can be calculated using the formula:

Time = Distance / Relative Speed

Substituting the values we have:

Time = D km / 20 km/h

To find the value of D, we need to consider the time it takes for the taxi to catch up to the bus. Let's assume this time is T hours.

We can now write the equation:

T = D / 20

To find the value of T, we need to solve this equation.

Calculation

To solve the equation, we need to find the value of T.

T = D / 20

We know that the interval between the bus and the taxi is 1 hour. Therefore, the time it takes for the taxi to catch up to the bus is 1 hour.

Substituting this value into the equation:

1 = D / 20

To find the value of D, we can multiply both sides of the equation by 20:

20 = D

Therefore, the distance between the bus and the taxi is 20 km.

Answer

The taxi will catch up to the bus in 1 hour.

Verification

To verify the answer, we can calculate the distance traveled by the bus and the taxi in 1 hour.

The bus travels at an average speed of 60 km/h, so in 1 hour, it will travel 60 km.

The taxi travels at an average speed of 80 km/h, so in 1 hour, it will travel 80 km.

Since the distance between the bus and the taxi is 20 km, the taxi will catch up to the bus in 1 hour.

Therefore, the answer is verified.

Conclusion

The taxi will catch up to the bus in 1 hour.