Question

Первую треть трассы велосипедист ехал со скоростью 12 км / ч , вторую треть -- со скоростью 16 км / ч , а последнюютреть -- со скоростью 24 км / ч . Найдите среднюю скорость велосипедиста на протяжении всего пути

Answer 1

Обозначим весь путь 3S

тогда

1 часть S       V =12 км/час     t= S/12
2 часть S       V=16 км/час      t= S/16
3 часть S       V=24 км/час      t=S/24

Общий путь 3S

общее время

$\displaystyle \frac{S}{12}+ \frac{S}{16}+ \frac{S}{24}= \frac{4S+3S+2S}{48}= \frac{9S}{48}$

тогда средняя скорость

$\displaystyle V= \frac{3S}{ \frac{9S}{48}}= \frac{48*3S}{9S}= \frac{48}{3}=16$

Ответ  16 км/час

Answer 2

Calculation of Average Speed

To find the average speed of the cyclist over the entire distance, we can use the formula:

Average Speed = Total Distance / Total Time

Let's calculate the average speed step by step.

1. First, we need to determine the total distance covered by the cyclist. We know that the cyclist traveled the first third of the distance at a speed of 12 km/h, the second third at a speed of 16 km/h, and the last third at a speed of 24 km/h.

Let's assume the total distance is D km. Therefore, each third of the distance would be D/3 km.

2. Next, we need to calculate the time taken for each third of the distance. We can use the formula:

Time = Distance / Speed

For the first third of the distance, the time taken would be (D/3) / 12 hours.

For the second third of the distance, the time taken would be (D/3) / 16 hours.

For the last third of the distance, the time taken would be (D/3) / 24 hours.

3. Finally, we can calculate the total time taken by summing up the times for each third of the distance.

Total Time = (D/3) / 12 + (D/3) / 16 + (D/3) / 24

Now, we can substitute the values into the formula for average speed:

Average Speed = D / [(D/3) / 12 + (D/3) / 16 + (D/3) / 24]

Simplifying the equation further, we get:

Average Speed = 1 / [(1/12) + (1/16) + (1/24)]

Let's calculate the average speed using this formula.

Calculation:

Using the formula mentioned above, we can calculate the average speed of the cyclist.

Average Speed = 1 / [(1/12) + (1/16) + (1/24)]

Calculating the values:

Average Speed = 1 / [(0.0833) + (0.0625) + (0.0417)]

Average Speed = 1 / (0.1875)

Average Speed ≈ 5.33 km/h

Therefore, the average speed of the cyclist over the entire distance is approximately 5.33 km/h.

Please note that the above calculation assumes that the cyclist traveled each third of the distance at a constant speed.