Question

Два велосипедиста одновременно отправились в 108-километровый пробег. Первый ехал со скоростью на 3 км/ч большей, чем скорость второго, и прибыл к финишу на 1 час 48 мин. раньше второго. Найдите скорость велосипедиста, пришедшего к финишу первым. Ответ дайте в км/ч.

Answer 1

Пусть скорость второго велосипедиста Х А первого Х+3 108/Х - 108/Х+3 = 1,8

Answer 2

пусть скорость велосипедиста прибывшего к финишу первым х км\ч, тогда скорость второго х-3 км\час. Время езды первого 108\х час, второго 108\(х-3). По условию задачи
108\(х-3)-108\х=1+48\60=108\60
1\(х-3)-1\х=1\60
60*(х-(х-3))=х(х-8)
60*3=х(х-3)
180=х^2-3x
x^2-3x-180=0
D=9+720=729
x1=(3-27)\2<0 - не подходит
х2=(3+27)\2=15
ответ: 15 км\час

Answer 3

Problem Analysis

We are given that two cyclists simultaneously started a 108-kilometer race. The first cyclist traveled at a speed 3 km/h faster than the second cyclist and arrived at the finish line 1 hour and 48 minutes earlier than the second cyclist. We need to find the speed of the cyclist who finished first.

Solution

Let's assume the speed of the second cyclist is x km/h. Then the speed of the first cyclist would be x + 3 km/h.

We can use the formula distance = speed × time to calculate the time taken by each cyclist to complete the race.

For the first cyclist: - Distance = 108 km - Speed = x + 3 km/h - Time = 108 / (x + 3) hours

For the second cyclist: - Distance = 108 km - Speed = x km/h - Time = 108 / x hours

According to the problem, the first cyclist arrived at the finish line 1 hour and 48 minutes earlier than the second cyclist. This can be written as:

108 / (x + 3) = 108 / x + 1 + 48/60

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can cross-multiply and simplify:

108x = 108(x + 3) + (1 + 48/60)x

Simplifying further:

108x = 108x + 324 + (1 + 48/60)x

Combining like terms:

108x - 108x = 324 + (1 + 48/60)x

Simplifying:

0 = 324 + (1 + 48/60)x

Subtracting 324 from both sides:

-(1 + 48/60)x = 324

Converting 1 hour and 48 minutes to hours:

-(1 + 48/60)x = 324

-1.8x = 324

Dividing both sides by -1.8:

x = -324 / 1.8

Calculating the value of x:

x = -180

Since the speed cannot be negative, we can ignore the negative sign and take the absolute value:

x = 180

Therefore, the speed of the cyclist who finished first is 180 km/h.

Answer

The speed of the cyclist who finished first is 180 km/h.