Question

От станции до турбазы 30 км. Из них 24 велосипедист проехал по шоссе с одной скоростью, а свернув на лесную дорогу, снизил скорость на 3 км/ч. Найдите скорость велосипедиста по шоссе, если на весь путь он затратил 2ч 40м Пожалуйста, со схемой и объяснением!! Очень нужно

Answer 1

Пусть велосипедист проехал по шоссе 24 км со скоростью x км\ч .

Тогда по лесной дороге он проехал (30 - 24) = 6 км со скоростью

(x - 3) км\ч .

На путь по шоссе велосипедист затратил :  24\x  часа , а на путь по лесной дороге  6\(x - 3) часа . На весь путь велосипедист затратил :

2ч 40 м = 2 2\3 часа . Составим и решим уравнение :

$\displaystyle\bf\\\frac{24}{x} +\frac{6}{x-3} =2\frac{2}{3} \\\\\\\frac{24}{x} +\frac{6}{x-3} -\frac{8}{3} =0\\\\\\\frac{24\cdot 3 \cdot (x-3)+6\cdot 3\cdot x-8\cdot x\cdot (x-3)}{3x(x-3)} =0\\\\\\\frac{72x-216+18x-8x^{2} +24x}{3x(x-3)} =0\\\\\\\frac{8x^{2} -114x+216}{3x(x-3)} =0\\\\\\8x^{2} -114x+216=0 \ \ , \ \ x\neq 0 \ \ , \ \ x\neq 3\\\\4x^{2} -57x+108=0\\\\D=(-57)^{2}-4\cdot 4 \cdot 108=3249-1728=1521 =39^{2} \\\\\\x_{1} =\frac{57+39}{8} =\frac{96}{8} =12$

$\displaystyle\bf\\x_{2} =\frac{57-39}{8} =\frac{18}{8} =2,25$

Ответ : скорость велосипедиста по шоссе равна 12 км\час .

Answer 2

Problem Analysis

We are given that the distance from the station to the tourist base is 30 km. Out of this distance, the cyclist traveled 24 km on the highway at a certain speed and then reduced their speed by 3 km/h when they turned onto a forest road. We need to find the speed of the cyclist on the highway.

Solution

Let's assume the speed of the cyclist on the highway is x km/h. Since the cyclist reduced their speed by 3 km/h on the forest road, their speed on the forest road would be (x - 3) km/h.

We know that the total time taken for the entire journey is 2 hours and 40 minutes, which is equivalent to 2.67 hours.

To find the speed on the highway, we can use the formula:

Speed = Distance / Time

Let's calculate the time taken for each part of the journey.

The time taken on the highway can be calculated as:

Time on highway = Distance on highway / Speed on highway

The time taken on the forest road can be calculated as:

Time on forest road = Distance on forest road / Speed on forest road

We can now set up the equation using