Question

Города А, В , С соеденены прямолинейным шоссе , причем город В рассположен между городами А и С . Из города А в сторону города С выехал легковой автомобиль ,и одновременно с ним из города В в сторону города С выехал грузовик . Через сколько часов после выезда легковой автомобиль догонит грузовик , если скорость легкового автомобиля на 23 км/ч больше скорости грузовика , а расстояние между городами ровно 92 км?

Answer 1

$92/23=4$ часа  легковой автомобиль догонит грузовик 

т к скорость легкового автомобиля на 23 км/ч больше скорости грузовика, то 23км/ч это скорость сближения

Answer 2

Problem Analysis

We are given three cities, A, B, and C, connected by a straight highway. City B is located between cities A and C. A car leaves city A towards city C, and at the same time, a truck leaves city B towards city C. The car's speed is 23 km/h faster than the truck's speed, and the distance between the cities is 92 km. We need to determine how many hours after the car's departure it will catch up to the truck.

Solution

To solve this problem, we can use the formula: time = distance / speed. We'll calculate the time it takes for both the car and the truck to reach city C, and then find the difference in their times.

Let's assume the speed of the truck is x km/h. Therefore, the speed of the car is x + 23 km/h.

The distance between city A and city B is not given, but we can assume it is the same as the distance between city B and city C, which is 92 km.

Using the formula, the time it takes for the car to reach city C is: time_car = distance / speed_car.

Similarly, the time it takes for the truck to reach city C is: time_truck = distance / speed_truck.

To find the time it takes for the car to catch up to the truck, we subtract the time it takes for the truck from the time it takes for the car: time_catch_up = time_car - time_truck.

Let's calculate the values:

1. Speed of the truck: x km/h. 2. Speed of the car: x + 23 km/h. 3. Distance between city B and city C: 92 km. 4. Time it takes for the car to reach city C: time_car = 92 / (x + 23) hours. 5. Time it takes for the truck to reach city C: time_truck = 92 / x hours. 6. Time it takes for the car to catch up to the truck: time_catch_up = time_car - time_truck hours.

Let's calculate the value of time_catch_up:

time_catch_up = (92 / (x + 23)) - (92 / x) hours.

Now we can solve this equation to find the value of x and then calculate the value of time_catch_up.

Calculation

Let's calculate the value of time_catch_up using the given equation.

time_catch_up = (92 / (x + 23)) - (92 / x) hours.

Since we don't have the exact values of the speeds of the car and the truck, we cannot calculate the exact value of time_catch_up. However, we can set up the equation and solve it using algebraic methods.

Let's simplify the equation:

time_catch_up = (92x - 92(x + 23)) / (x(x + 23)) hours.

Simplifying further:

time_catch_up = (92x - 92x - 2116) / (x^2 + 23x) hours.

time_catch_up = -2116 / (x^2 + 23x) hours.

Since we don't have the exact values of the speeds of the car and the truck, we cannot calculate the exact value of time_catch_up. However, we can conclude that the time it takes for the car to catch up to the truck will be negative, indicating that the car will not catch up to the truck.

Therefore, based on the given information, the car will not catch up to the truck.

Answer

Based on the given information, the car will not catch up to the truck.

Please let me know if I can help you with anything else.