Question

Турист шел от турбазы до станции со скоростью 6км/ч. Если бы он шел со скоростью 4км/ч, то затратил бы на дорогу на 1 час больше. Чему равно расстояние от турбазы до станции?

Answer 1

S - расстояние от турбазы до станции
v₁ = 6 км/ч
t₁ = S/v₁ - время движения при скорости 6 км/ч
v₂ = 4 км/ч
t₂ = t₁+1 = S/v₂ - время движения при скорости 4 км/ч

Тогда: { t₂ = S/v₁ + 1   
            { t₂ = S/v₂        =>    S/v₁ + 1 = S/v₂
                                             S/6 - S/4 = -1
                                             (2S-3S)/12 = -1
                                             S/12 = 1
                                             S = 12 (км)

Ответ: 12 км
                                            

Answer 2

Calculation of the Distance from the Tourist Base to the Station

To calculate the distance from the tourist base to the station, we can use the information provided in the question. Let's break down the given information:

- The tourist walks from the tourist base to the station at a speed of 6 km/h. - If the tourist walked at a speed of 4 km/h, it would take 1 hour longer to reach the station.

Let's assume that the distance from the tourist base to the station is d kilometers.

If the tourist walks at a speed of 6 km/h, the time taken to reach the station would be d/6 hours.

If the tourist walks at a speed of 4 km/h, the time taken to reach the station would be d/4 hours.

According to the given information, if the tourist walked at a speed of 4 km/h, it would take 1 hour longer to reach the station. Therefore, we can set up the following equation:

d/4 = d/6 + 1

To solve this equation, we can multiply both sides by 12 to eliminate the denominators:

3d = 2d + 12

Simplifying the equation, we get:

d = 12

Therefore, the distance from the tourist base to the station is 12 kilometers.