Question

Путешественник предполагал пройти 30 км. с некоторой скоростью. Но с этой скоростью он шел всего 1 час, а затем стал проходить в час на 1 км. меньше. В результате он прибыл в конечный пункт на 48 мин. позднее, чем предполагал. С какой скоростью (км\ч) путешественник предполагал пройти путь?

Answer 1

V -ожидаемая скорость

t - ожидаемое время

S - 30 км

Ожидалось:

S = Vt

Получилось:

S = V * 1 + (V - 1)(t - 1 + 48/60)  = V + (V - 1)(t - 1/5) = V + Vt - V/5 - t +1/5

Vt = V + Vt - V/5 - t + 1/5

t = 4/5V + 1/5

 

V = S/ t = 30 / t

Подставляем:

t = 4 * 30 / 5t + 1/5

t = 24/t + 1/5

$5t^{2}-t-120=0$

t = 5

Значит V = 30 / 5 = 6

 

Answer 2

Problem Analysis

The traveler initially planned to cover a distance of 30 km at a certain speed. However, after walking for 1 hour, the traveler reduced their speed by 1 km/h. As a result, they arrived at their destination 48 minutes later than expected. We need to determine the speed at which the traveler initially planned to cover the distance.

Solution

Let's break down the problem and solve it step by step:

1. Let's assume the initial speed of the traveler was x km/h. 2. The traveler walked at this speed for 1 hour, covering a distance of x km. 3. After 1 hour, the traveler reduced their speed by 1 km/h, so their new speed was (x - 1) km/h. 4. The remaining distance to be covered is (30 - x) km. 5. The traveler covered this remaining distance at a speed of (x - 1) km/h. 6. The total time taken for the remaining distance is given by the formula: ``` Time = Distance / Speed ``` So, the time taken to cover the remaining distance is: ``` Time = (30 - x) / (x - 1) hours ``` 7. The total time taken for the entire journey is the sum of the time taken for the initial distance and the time taken for the remaining distance: ``` Total Time = 1 hour + (30 - x) / (x - 1) hours ``` 8. The traveler arrived at the destination 48 minutes later than expected, which is equal to 48/60 = 0.8 hours. 9. Therefore, we can set up the equation: ``` Total Time = 1 hour + (30 - x) / (x - 1) hours = 1.8 hours ``` 10. Now, we can solve this equation to find the value of x.

Let's solve the equation:

1 + (30 - x) / (x - 1) = 1.8

Simplifying the equation:

(30 - x) / (x - 1) = 0.8
30 - x = 0.8(x - 1)
30 - x = 0.8x - 0.8
1.8x = 30.8
x = 30.8 / 1.8
x ≈ 17.11

Therefore, the traveler initially planned to cover the distance at a speed of approximately 17.11 km/h.

Note: The above solution assumes that the traveler maintained a constant speed throughout each hour of the journey. If there were variations in speed within each hour, the calculation would be more complex.

Answer

The traveler initially planned to cover the distance at a speed of approximately 17.11 km/h.