Question

Автобус ехал по городу со скорость 50 км/ч некоторое время. Затем он ехал в 2 раза быстрее по международной трассе в соседний город, на что времени у него ушло в 3 раза больше того, что он ехал по городу. На весь путь он потратил час. Сколько километров проехал автобус за этот час?

Answer 1

50*2=100(км/ч)-скорость по трассе

х(ч) - по городу

3х(ч) - по трассе

получается:

х+3х=1

4х=1

х=1/4(ч)-по городу

1/4*3=0,75 (ч) - по трассе

0,25*50=12,5(км)-по городу

0,75*100=75(км)-по трассе

12,5+75=87,5(км)-проехал автобус за час

Answer 2

Problem Analysis

We are given that a bus traveled at a speed of 50 km/h for some time within a city. Then, it traveled at twice the speed on an international highway to a neighboring city, taking three times longer than the time spent in the city. The total travel time was one hour. We need to determine how many kilometers the bus traveled in that hour.

Solution

Let's assume that the time the bus traveled within the city is t hours. Therefore, the time it traveled on the international highway is 3t hours.

We can calculate the distance traveled within the city using the formula distance = speed × time. Since the speed within the city is 50 km/h and the time is t hours, the distance traveled within the city is 50t kilometers.

Similarly, we can calculate the distance traveled on the international highway using the same formula. Since the speed on the international highway is twice the speed within the city (i.e., 2 × 50 = 100 km/h) and the time is 3t hours, the distance traveled on the international highway is 100(3t) = 300t kilometers.

The total distance traveled by the bus is the sum of the distances traveled within the city and on the international highway. Therefore, the total distance is 50t + 300t = 350t kilometers.

We are given that the total travel time is one hour. Therefore, the sum of the time spent within the city (t) and the time spent on the international highway (3t) is equal to one hour:

t + 3t = 1

Simplifying the equation, we get:

4t = 1

Solving for t, we find:

t = 1/4 hours

Substituting this value back into the equation for the total distance, we can calculate the distance traveled by the bus in one hour:

distance = 350t = 350(1/4) = 87.5 kilometers.

Therefore, the bus traveled 87.5 kilometers in one hour.

Answer

The bus traveled 87.5 kilometers in one hour.

Explanation

The bus traveled at a speed of 50 km/h for some time within the city. Then, it traveled at twice the speed on an international highway to a neighboring city, taking three times longer than the time spent in the city. The total travel time was one hour. To calculate the distance traveled by the bus in one hour, we used the formula distance = speed × time. By substituting the given values and solving the equations, we found that the bus traveled 87.5 kilometers in one hour.