Question

расстояние между двумя городами автобус преодаливает за 5,75часов , а автомобиль, скорость каторова на 10,5 км/ч больше -за 5 часов . опредилите скорость автомобиля и растояние между городами?

Answer 1

Problem Analysis

To solve this problem, we need to find the speed of the car and the distance between the two cities. We are given that a bus covers the distance in 5.75 hours, while a car, which is 10.5 km/h faster, covers the same distance in 5 hours.

Calculation

Let's assume the speed of the car is x km/h. Since the car is 10.5 km/h faster than the bus, the speed of the bus would be x - 10.5 km/h.

We can use the formula distance = speed × time to calculate the distance between the two cities.

For the bus: distance = (x - 10.5) km/h × 5.75 hours

For the car: distance = x km/h × 5 hours

Since the distances covered by the bus and the car are the same, we can set up the following equation:

(x - 10.5) km/h × 5.75 hours = x km/h × 5 hours

Now, let's solve this equation to find the value of x.

Solution

Expanding the equation, we get:

5.75x - 59.625 = 5x

Simplifying the equation, we get:

0.75x = 59.625

Dividing both sides of the equation by 0.75, we get:

x = 79.5

Therefore, the speed of the car is 79.5 km/h.

To find the distance between the two cities, we can substitute the value of x into either of the distance formulas. Let's use the formula for the car:

distance = 79.5 km/h × 5 hours

Calculating the distance, we get:

distance = 397.5 km

Therefore, the distance between the two cities is 397.5 km.

Conclusion

The speed of the car is 79.5 km/h and the distance between the two cities is 397.5 km.