Question

Вася решил сходить в магазин, который расположен на расстоянии 4 км от дома Васи. на пути из магазина домой Вася шёл со скоростью на 3 км/ч меньше, чем по пути в магазин. вернувшись домой, Вася обнаружил, что на весь путь он потратил 5 часов. определи, с какой скоростью Вася шёл в магазин. ​

Answer 1

Ответ:

10 км

Пошаговое объяснение:

5 км/ч = 5 км за час. => за два часа пройдено 10км.

Answer 2

Problem Analysis

Vasya went to a store located 4 km away from his house. On the way back from the store to his house, Vasya walked at a speed 3 km/h slower than on the way to the store. It took him a total of 5 hours for the entire trip. We need to determine Vasya's speed while walking to the store.

Solution

Let's assume Vasya's speed while walking to the store is x km/h. Since his speed on the way back is 3 km/h slower, his speed while walking back is (x - 3) km/h.

To find the time it took Vasya to walk to the store, we can use the formula:

Time = Distance / Speed

The distance from Vasya's house to the store is 4 km. Therefore, the time taken to walk to the store is:

Time to store = 4 km / x km/h

On the way back, Vasya walked at a speed of (x - 3) km/h. The distance from the store to Vasya's house is also 4 km. Therefore, the time taken to walk back is:

Time back = 4 km / (x - 3) km/h

The total time for the entire trip is given as 5 hours. Therefore, we can write the equation:

Time to store + Time back = 5 hours

Substituting the values, we get:

(4 km / x km/h) + (4 km / (x - 3) km/h) = 5 hours

To solve this equation, we can multiply both sides by x(x - 3) to eliminate the denominators:

4(x - 3) + 4x = 5x(x - 3)

Simplifying the equation:

4x - 12 + 4x = 5x^2 - 15x

8x - 12 = 5x^2 - 15x

5x^2 - 23x + 12 = 0

Now we can solve this quadratic equation to find the value of x, which represents Vasya's speed while walking to the store.

Quadratic Equation Solution

Using the quadratic formula, we can find the values of x that satisfy the equation:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 5, b = -23, and c = 12. Substituting these values into the quadratic formula:

x = (-(-23) ± √((-23)^2 - 4 * 5 * 12)) / (2 * 5)

Simplifying:

x = (23 ± √(529 - 240)) / 10

x = (23 ± √289) / 10

x = (23 ± 17) / 10

This gives us two possible values for x:

x1 = (23 + 17) / 10 = 4 km/h

x2 = (23 - 17) / 10 = 1.6 km/h

Since Vasya's speed cannot be negative, we can discard the second solution. Therefore, Vasya's speed while walking to the store is 4 km/h.

Answer

Vasya walked to the store at a speed of 4 km/h.

Verification

Let's verify our answer using the given information. According to the problem, Vasya walked 4 km to the store and 4 km back to his house. The time taken to walk to the store at a speed of 4 km/h is:

Time to store = 4 km / 4 km/h = 1 hour

On the way back, Vasya walked at a speed of (4 - 3) km/h, which is 1 km/h. The time taken to walk back is:

Time back = 4 km / 1 km/h = 4 hours

The total time for the entire trip is 5 hours, which matches the given information. Therefore, our answer is verified.

Conclusion

Vasya walked to the store at a speed of 4 km/h.