Question

От поселка до турбазы, двигаясь в гору, велосипедист доехал за 3 ч. При возвращении его средняя скорость оказалась на 6 км\ч больше, поэтому дорога заняла у его на 1 ч меньше. Найдите, на каком расстоянии от поселка расположена турбаза.

Answer 1

Пусть: Х км/ч скорость движения велосипедиста в гору.тогда (Х + 6) км/ч - скорость движения велосипедиста с горы,3*X км - расстояние от поселка до турбазы,(Х + 6)*2 - расстояние от турбазы до поселка.По условию задачи состовим уравнение:3*X = (X + 6)*23X = 2X + 123X - 2X = 12X = 1212 км/ч скорость в гору.12*3 = 36 км расстояние от поселка до турбазы.Ответ: 36 км расстояние от поселка до турбазы.

Answer 2

Problem Analysis

The cyclist traveled from the settlement to the tourist base uphill in 3 hours. On the return journey, his average speed was 6 km/h faster, and the trip took 1 hour less. We need to find the distance from the settlement to the tourist base.

Solution

Let's denote the distance from the settlement to the tourist base as D.

The time taken to travel from the settlement to the tourist base is 3 hours, and the time taken for the return journey is 3 - 1 = 2 hours.

We can use the formula: time = distance / speed.

For the first journey: - Time = 3 hours - Speed = D / S, where S is the speed for the first journey

For the return journey: - Time = 2 hours - Speed = D / (S + 6), where S + 6 is the speed for the return journey

We can set up the following equations: 1. 3 = D / S 2. 2 = D / (S + 6)

We can solve these equations to find the value of D.

Calculations

Let's solve the equations to find the value of D.

From equation 1: D = 3S

From equation 2: D = 2(S + 6)

Equating the two expressions for D: 3S = 2(S + 6)

Solving for S: 3S = 2S + 12 S = 12

Substitute S = 12 into equation 1: D = 3 * 12 D = 36

Answer

The tourist base is located at a distance of 36 km from the settlement.