Question

Сергей ходит от дома до стадиона пешком со скоростью 4 км/ч. Однажды он отправился из дома в обычное время, но поехал на велосипеде со скоростью 12 км/ч. На стадион он приехал на 15 мин раньше обычного. Чему равно расстояние от дома до стадиона.

Answer 1

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Answer 2

Problem Analysis

Sergey usually walks from home to the stadium at a speed of 4 km/h. However, one day he rode his bicycle at a speed of 12 km/h and arrived at the stadium 15 minutes earlier than usual. We need to determine the distance from Sergey's home to the stadium.

Solution

Let's assume that the usual time it takes Sergey to travel from home to the stadium is t hours. We can use the formula distance = speed × time to calculate the distance.

When Sergey walks at a speed of 4 km/h, the distance can be calculated as 4t km.

When Sergey rides his bicycle at a speed of 12 km/h, the distance can be calculated as 12(t - 15/60) km, since he arrived 15 minutes earlier than usual.

To find the distance from Sergey's home to the stadium, we can equate the two distances and solve for t.

Calculation

Let's solve the equation:

4t = 12(t - 15/60)

First, let's simplify the equation:

4t = 12t - 3

Now, let's isolate t:

4t - 12t = -3

-8t = -3

Dividing both sides by -8:

t = -3 / -8

t = 3/8

So, it takes Sergey 3/8 hours to travel from home to the stadium.

Now, let's calculate the distance using the formula distance = speed × time.

When Sergey walks at a speed of 4 km/h, the distance is:

distance = 4 × (3/8) = 12/8 = 1.5 km

Therefore, the distance from Sergey's home to the stadium is 1.5 km.

Answer

The distance from Sergey's home to the stadium is 1.5 km.