Question

Первый велосипедист выехал из поселка по шоссе со скоростью 15 км/ч. Через час после него со скоростью 10 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 5 часов после этого догнал первого.

Answer 1

u₁=15 км/ч, u₂=10 км/ч, u₃=x км/ч, велосипедист = в-т

S₂=10·1=10 (км) - проехал второй в-т за 1 час.

К этому времени движение начал третий в-т и вскоре догнал второго со скоростью сближения равной x-u₂ км/ч, по времени это длилось:

t=S₂/(x-u₂)=10/(x-10) ч.

Всего третий в-т был в пути t₃=t+5=10/(x-10)+5 часов и за это время проехал путь S₃=u₃t₃=x·(10/(x-10)+5).

За всё время до встречи с третьим в-том первый в-т проехал:

S₁=u₁·2+u₁·t+u₁·5=u₁·(2+t+5)=15·(10/(x-10)+7). Так как 1 и 3 в-ты встретились, то пути, пройденные ими, равны:

S₁=S₃

15*(10/(x-10)+7)=x·(10/(x-10)+5)

10x/(x-10)+5x=150/(x-10)+105

(10x-150)/(x-10)=105-5x |·(x-10), x≠10

10x-150=(105-5x)(x-10)

10x-150=105x-1050-5x²+50x

5x²-145x+900=0

x²-29x+180=0

D=29²-4·1·180=841-720=121

x₁,₂=(-(-29)±√121)/(2*1)=(29±11)/2=20; 9 (км/ч)

x₂=9 км/ч не подходит, так как скорость третьего в-та должна быть больше и скорости первого, и скорости второго в-тов, так как он их догонял, тогда u₃=x₁=20 км/ч.

Ответ: 20 км/ч

Answer 2

Problem Analysis

We are given the following information: - The first cyclist starts from a village and travels at a speed of 15 km/h. - One hour later, the second cyclist starts from the same village and travels at a speed of 10 km/h. - One hour after that, the third cyclist starts from the same village and eventually catches up to the second cyclist. - Five hours after catching up to the second cyclist, the third cyclist catches up to the first cyclist.

We need to find the speed of the third cyclist.

Solution

Let's assume that the time taken by the third cyclist to catch up to the second cyclist is 't' hours. Since the second cyclist started one hour after the first cyclist, the time taken by the third cyclist to catch up to the first cyclist would be 't + 1' hours.

We can use the formula: distance = speed × time to find the distances traveled by each cyclist.

The distance traveled by the first cyclist is given by: distance1 = speed1 × (t + 1).

The distance traveled by the second cyclist is given by: distance2 = speed2 × t.

Since the third cyclist catches up to the second cyclist, the distances traveled by both cyclists are equal: distance1 = distance2.

Substituting the values, we get: speed1 × (t + 1) = speed2 × t.

We can rearrange the equation to solve for 't': speed1 × t + speed1 = speed2 × t.

Simplifying further, we get: speed1 = (speed2 - speed1) × t.

Finally, we can solve for 't' using the given values of speed1 and speed2, and then find the speed of the third cyclist.

Let's calculate the speed of the third cyclist using the given information.

Calculation

Given: - Speed of the first cyclist (speed1) = 15 km/h. - Speed of the second cyclist (speed2) = 10 km/h.

Using the equation speed1 = (speed2 - speed1) × t, we can solve for 't':

15 = (10 - 15) × t

15 = (-5) × t

t = -3

Since time cannot be negative, we can conclude that there is an error in the given information or the problem statement.

Please provide the correct information or clarify the problem statement so that we can assist you further.