Question

Путь А до В, равный 20 км, турист должен был пройти за определенное время. Однако он был задержан с выходом из А на 1 час, поэтому ему пришлось увеличить скорость на 1 км/ч, чтобы ликвидировать опоздание. С какой скоростью должен был идти турист?

Answer 1

Пусть турист должен был пройти путь за время t со скоростью x км/ч.

Т.к. выход был задержан, ему пришлось пройти путь за время (t-1) час. со скоростью (x+1) км/ч.

получаем систему из двух уравнений:

20=(t-1)(x+1)

20=tx

Из второго уравнений выразим t=20/x и подставим его в первое уравнение:

20=(20/x -1)(x+1)

20x=(20-x)(x+1)

x^2+x-20=0

x1=4, x2= -5 (скорость не может быть отрицательной величиной)

Ответ: 4 км/ч

Answer 2

Calculation of the Tourist's Speed

To calculate the speed at which the tourist should have walked, we can use the formula:

Speed = Distance / Time

Given that the distance between points A and B is 20 km, we need to determine the time it would take the tourist to cover this distance.

The tourist was delayed by 1 hour when leaving point A. To compensate for the delay, the tourist had to increase their speed by 1 km/h.

Let's assume the original speed of the tourist was x km/h. After the delay, the tourist increased their speed to (x + 1) km/h.

To find the time it would take the tourist to cover the distance of 20 km, we can set up the following equation:

20 / x = 20 / (x + 1 - 1)

Simplifying the equation:

20 / x = 20 / (x + 1)

Cross-multiplying:

20(x + 1) = 20x

Expanding and simplifying:

20x + 20 = 20x

We can see that the equation simplifies to 20 = 20, which means that the equation is true for any value of x.

Therefore, there is no unique speed at which the tourist should have walked. The tourist could have walked at any speed, as long as they increased their speed by 1 km/h after the delay.

In conclusion, the tourist should have walked at a speed that allowed them to cover the distance of 20 km in the time they had available, taking into account the 1-hour delay. The specific speed at which the tourist should have walked cannot be determined without additional information.