Question

Первый велосипедист выехал из поселка по шоссе со скоростью 18 км/ч. Через час после него со скоростью 16 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 4 часа после этого догнал первого. Ответ дайте в км/ч.

Answer 1

Х км/ч скорость 3-его вел-та
У ч время, чтобы догнать второго
16 км/ч скорость 2-ого вел-та
(У+1) ч время 2-ого до того, как его догнал 3-ий
Значит до встречи 3-ий проехал ху км, а второй проехал 16(у+1) км.
1-ое уравнение: ху=16(у+1)
(У+4) ч время до того, как догнал первого
(2+у+4=у+6) ч время 1-ого до того, как его догнал 3-ий.
Значит до встречи 3-ий проехал х(у+4) км, а первый проехал 18(у+6) км.
2-ое уравнение: х(у+4)=18(у+6)
Из первого: х=16(у+1)/у=(16у+16)/у
Подставим:(16у+16)(у+4)/у=18(у+6)
16у²+16у+64у+64=18у²+108у
2у²+28у-64=0
у²+14у-32=0
D=196+128=324
у=(-14+18)/2=2 ч
х=(16*2+16)/2=48/2=24 км/ч
Ответ: 24 км/ч

Answer 2

Problem Analysis

We are given the speeds of three cyclists who start from the same village and travel in the same direction. The third cyclist catches up with the second cyclist first and then catches up with the first cyclist later. We need to find the speed of the third cyclist.

Solution

Let's assume the speed of the third cyclist is x km/h.

The first cyclist travels for 1 hour at a speed of 18 km/h. Therefore, the distance covered by the first cyclist is 18 km.

The second cyclist starts 1 hour after the first cyclist and travels at a speed of 16 km/h. When the second cyclist starts, the first cyclist is already 18 km ahead. To catch up with the first cyclist, the second cyclist needs to cover this distance. The time it takes for the second cyclist to catch up with the first cyclist is given by the formula:

time = distance / speed

Substituting the values, we have:

time = 18 km / 16 km/h = 1.125 hours

Now, let's consider the third cyclist. The third cyclist starts 1 hour after the second cyclist and catches up with the second cyclist first. The time it takes for the third cyclist to catch up with the second cyclist is also 1.125 hours.

After catching up with the second cyclist, the third cyclist continues riding for 4 more hours and catches up with the first cyclist. Therefore, the total time taken by the third cyclist to catch up with both the second and first cyclists is:

total time = 1.125 hours + 4 hours = 5.125 hours

During this time, the third cyclist covers a distance equal to the distance covered by the first cyclist in 5.125 hours at a speed of x km/h.

Using the formula distance = speed * time, we can calculate the distance covered by the first cyclist:

distance = 18 km/h * 5.125 hours = 92.25 km

Since the third cyclist catches up with the first cyclist, the distance covered by the third cyclist is also 92.25 km.

Now, we can calculate the speed of the third cyclist using the formula speed = distance / time:

x km/h = 92.25 km / 5.125 hours

Calculating this, we find that the speed of the third cyclist is approximately 17.98 km/h.

Therefore, the speed of the third cyclist is approximately 17.98 km/h.

Answer

The speed of the third cyclist is approximately 17.98 km/h.