Question

Первый велосипедист выехал из поселка по шоссе со скоростью 17 км/ч. Через час после него со скоростью 13 км/ч из того же поселка в том же направлении выехал второй велосипедист, а еще через час после этого – третий. Найдите скорость третьего велосипедиста, если сначала он догнал второго, а через 3 часа 10 минут после этого догнал первого. Ответ дайте в км/ч.

Answer 1

За 2 часа первый проехал
s1 =v1*t1 = 17*2 = 34  км
Это расстояние третий "нагнал" за 3 часа 10 минут за счет увеличения скорости
V3= V1 +s1/t2 = 17+ 34/( 3 1/6)  = 17 + 10 14/19=27,737 км/ч - ОТВЕТ.
ПРОВЕРКА
Первый ехал 2+3 1/6 =5 1/6 час со  скоростью 17 км/ч = 87 5/6 км
Третий - 3 1/6 * 27 14/19 = 87 5/6 км
А второй - просто не причём. Он его догнал через t = 13/(27 14/19 - 13) = 247/280 час ~ 53 мин

Answer 2

Calculating the Speed of the Third Cyclist

To calculate the speed of the third cyclist, we can use the information provided and apply the principles of relative motion.

The first cyclist travels at a speed of 17 km/h. The second cyclist travels at a speed of 13 km/h.

Let's calculate the speed of the third cyclist.

Step 1: Finding the Time Taken by the Third Cyclist to Catch the Second Cyclist

The third cyclist catches the second cyclist after 3 hours and 10 minutes. This can be converted to 3.167 hours.

Step 2: Calculating the Distance Covered by the Third Cyclist to Catch the Second Cyclist

The distance covered by the third cyclist to catch the second cyclist can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \]

The distance covered by the second cyclist in 3.167 hours at a speed of 13 km/h is: \[ \text{Distance} = 13 \, \text{km/h} \times 3.167 \, \text{h} = 41.191 \, \text{km} \]

Step 3: Finding the Time Taken by the Third Cyclist to Catch the First Cyclist

The third cyclist catches the first cyclist after 3 hours.

Step 4: Calculating the Distance Covered by the Third Cyclist to Catch the First Cyclist

The distance covered by the third cyclist in 3 hours at an unknown speed can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \]

The distance covered by the first cyclist in 3 hours at a speed of 17 km/h is: \[ \text{Distance} = 17 \, \text{km/h} \times 3 \, \text{h} = 51 \, \text{km} \]

Step 5: Calculating the Speed of the Third Cyclist

Now, we can calculate the speed of the third cyclist using the distance covered to catch the second cyclist and the distance covered to catch the first cyclist.

The total distance covered by the third cyclist is the sum of the distances covered to catch the second and first cyclists: \[ 41.191 \, \text{km} + 51 \, \text{km} = 92.191 \, \text{km} \]

The total time taken by the third cyclist to cover this distance is: \[ 3.167 \, \text{h} + 3 \, \text{h} = 6.167 \, \text{h} \]

Therefore, the speed of the third cyclist is: \[ \text{Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{92.191 \, \text{km}}{6.167 \, \text{h}} \approx 14.96 \, \text{km/h} \]

The speed of the third cyclist is approximately 14.96 km/h.