Question

Решите задачу: ИЗ города А выехал автомобиль со скаростью 48км/ч. Через полора часа в том же направлении выехал второй автомобиль,скорость которого в 1целую три восьмых раза больше скорости первого.На каком расстоянии от города А второй автомобиль догонит первый?

Answer 1

48*1 3/8=48*11/8=6*11=66км/ч- скорость второго

х- время движения 2го до встречи

48(х+1,5)=66х
48х+72=66х
18х=72
х=72/18=4ч

66*4=264км-расстоянии от города А до места встречи

Answer 2

Problem Analysis

To solve this problem, we need to determine the distance at which the second car catches up to the first car. We are given the initial speed of the first car and the ratio of the second car's speed to the first car's speed. We can use this information to calculate the time it takes for the second car to catch up to the first car, and then use this time to find the distance traveled by both cars.

Solution

Let's break down the problem step by step:

1. We are given that the first car starts from city A with a speed of 48 km/h. 2. After half an hour (0.5 hours), the second car starts from the same city in the same direction. 3. The speed of the second car is 1 and 3/8 times the speed of the first car. To calculate the speed of the second car, we can multiply the speed of the first car by 1.375 (1 + 3/8). 4. We need to find the distance at which the second car catches up to the first car.

Let's calculate the time it takes for the second car to catch up to the first car:

- The time taken by the first car to cover a certain distance is the same as the time taken by the second car to cover the same distance, as they are traveling in the same direction. - Let's assume the time taken by both cars to meet is 't' hours. - The first car travels for 't' hours at a speed of 48 km/h, so the distance covered by the first car is 48t km. - The second car travels for 't - 0.5' hours at a speed of 48 * 1.375 km/h, so the distance covered by the second car is 66t - 33 km.

Now, we can set up an equation to find the value of 't':

48t = 66t - 33

Solving this equation, we find:

18t = 33

t = 33/18 = 11/6 hours

Now, let's calculate the distance at which the second car catches up to the first car:

- The distance covered by the first car in 11/6 hours is 48 * (11/6) km. - The distance covered by the second car in (11/6) - 0.5 hours is 66 * (11/6) - 33 km.

Therefore, the distance at which the second car catches up to the first car is:

48 * (11/6) - (66 * (11/6) - 33) km.

Let's calculate this:

48 * (11/6) - (66 * (11/6) - 33) = 88 km.

Answer: The second car will catch up to the first car at a distance of 88 km from city A.

Conclusion

In this problem, we calculated the distance at which the second car catches up to the first car. We used