Question

Путник шел в гору со скоростью 3 км/ч, а с горы 5 км/ч. Путь в гору на 1 км больше чем путь с горы. Затрачено 3 часа. Нужно найти весь путь

Answer 1

Х путь в гору
х-1  путь с горы
х/3 время в гору
(х-1)/5 время с горы
х/3+(х-1)/5=3
5х+3х-3=45
8х=48
х=6км путь в гору
6-1=5км путь с горы
6+5=11км весь путь

Answer 2

Problem Analysis

We are given that a traveler walks uphill at a speed of 3 km/h and downhill at a speed of 5 km/h. The distance uphill is 1 km longer than the distance downhill. The traveler spends a total of 3 hours on the journey. We need to find the total distance traveled.

Solution

Let's assume the distance traveled downhill is x km. Since the distance uphill is 1 km longer, the distance uphill is x + 1 km.

We can calculate the time spent uphill and downhill using the formula: time = distance / speed.

The time spent uphill is (x + 1) / 3 hours, and the time spent downhill is x / 5 hours.

According to the problem, the total time spent on the journey is 3 hours. Therefore, we can write the equation:

(x + 1) / 3 + x / 5 = 3

To solve this equation, we can multiply through by the least common multiple (LCM) of the denominators, which is 15:

5(x + 1) + 3x = 45

Simplifying the equation:

5x + 5 + 3x = 45

8x + 5 = 45

8x = 40

x = 5

Now that we have the value of x, we can find the distance traveled uphill and downhill:

Distance uphill = x + 1 = 5 + 1 = 6 km

Distance downhill = x = 5 km

The total distance traveled is the sum of the distances uphill and downhill:

Total distance = 6 km + 5 km = 11 km

Therefore, the traveler traveled a total distance of 11 km.

Answer

The traveler traveled a total distance of 11 km.