Question

ПОМОГИТЕ ПОЖАЛУЙСТА!! Реши задачу.От города до турбазы, двигаясь в гору, велосипедист доехал за 3 часа.При возвращении его средняя скорость оказалась на 10 км/ч больше, поэтому дорога заняла у него на 1 час меньше. Вычисли, расстояние от города до турбазы.

Answer 1

Problem Analysis

We are given that a cyclist traveled from a city to a tourist base. On the way up, the cyclist took 3 hours to reach the base. On the return journey, the cyclist's average speed was 10 km/h higher, and the journey took 1 hour less. We need to calculate the distance from the city to the tourist base.

Solution

Let's assume the distance from the city to the tourist base is d km.

On the way up, the cyclist took 3 hours to cover the distance, so the average speed on the way up was d/3 km/h.

On the return journey, the cyclist's average speed was 10 km/h higher, so the average speed on the return journey was (d/3) + 10 km/h. The journey took 1 hour less, so the time taken on the return journey was 3 - 1 = 2 hours.

We can use the formula speed = distance/time to calculate the distance.

For the way up: d/3 = (d/3) km/h * 3 hours

For the return journey: d/2 = [(d/3) + 10] km/h * 2 hours

Now, we can solve these two equations to find the value of d, which represents the distance from the city to the tourist base.

Let's solve the equations step by step:

1. Multiply both sides of the equation for the way up by 3: d = (d/3) km/h * 3 hours Simplifying, we get: d = d km/h * 3 hours / 3 d = d km/h * 1 hour

2. Multiply both sides of the equation for the return journey by 2: d/2 = [(d/3) + 10] km/h * 2 hours Simplifying, we get: d/2 = (d/3 + 10) km/h * 2 hours d/2 = (2/3)d km/h + 20 km/h * 2 hours d/2 = (2/3)d km/h + 40 km

3. Multiply both sides of the equation for the return journey by 2/3 to eliminate the fraction: (2/3)(d/2) = (2/3)(2/3)d km/h + (2/3)40 km Simplifying, we get: d/3 = (4/9)d km/h + 80/3 km d/3 - (4/9)d km/h = 80/3 km (9d - 4d)/27 = 80/3 km 5d/27 = 80/3 km

4. Multiply both sides of the equation by 27/5 to solve for d: d = (80/3 km) * (27/5) Simplifying, we get: d = 144 km

Therefore, the distance from the city to the tourist base is 144 km.

Answer

The distance from the city to the tourist base is 144 km.