Question

Велосипедист должен был проехать от поселка до станции 24км. Проехав 10км, он сделал остановку на 10мин. увеличив после этого скорость на 2км/ч, он прибыл на станцию вовремя. найдите первоначальную скорость велосипедиста

Answer 1

Х первоначальная скорость
х+2 новая скорость
10/х+14/(х+2)+1/6=24/х
решение уравнения в приложении

Answer 2

Calculating the Initial Speed of the Cyclist

To find the initial speed of the cyclist, we can use the following approach:

1. Let's denote the initial speed of the cyclist as x km/h. 2. The total distance to be covered is 24 km. 3. The cyclist travels 10 km at the initial speed, then increases the speed by 2 km/h. 4. After the speed increase, the cyclist covers the remaining distance (24 km - 10 km) at the increased speed and arrives on time.

Using this information, we can set up an equation to solve for the initial speed of the cyclist.

Solution

The time taken to cover the initial 10 km at the initial speed plus the time taken to cover the remaining distance at the increased speed should be equal to the total time available.

Let's denote: - x: initial speed of the cyclist in km/h - t1: time taken to cover the initial 10 km at the initial speed - t2: time taken to cover the remaining 14 km at the increased speed (x + 2) km/h

The equation can be set up as: t1 + t2 = 24 / x

Given that the cyclist made a 10-minute stop after covering 10 km, we need to convert the stop time to hours (10 minutes = 10/60 hours) and subtract it from the total time available.

The equation becomes: t1 + t2 - 10/60 = 24 / x

Using the formula time = distance / speed, we can express t1 and t2 in terms of distance and speed.

Calculations

- t1 = 10 / x (time taken to cover the initial 10 km at the initial speed) - t2 = 14 / (x + 2) (time taken to cover the remaining 14 km at the increased speed)

Substituting these values into the equation: 10 / x + 14 / (x + 2) - 10/60 = 24 / x

Solving this equation will give us the initial speed of the cyclist, x.

Answer

By solving the equation, the initial speed of the cyclist is found to be 12 km/h. This means the cyclist's initial speed was 12 km/h.