Question

два велосипедиста одновременно отправлялись в 96 километровый пробег.Первый ехал со скоростью,на 4км/ч больше,чем скорость второго,и прибыл к финишу на 4 часа раньше второго.Найдите скорость велосипедиста,пришедшего к финишу вторым.Ответ дайте в км/ч

Answer 1

Второй ехал со скоростью x, значит первый: x + 4

Всю дорогу первый прошел за 96/(x+4)  часа, а второй за 96/x часа

Значит:

4 + 96/(x+4) = 96/x

Приведем к общему знаменателю:

(4x + 16 + 96)/(x+4) = 96/x

Вынесем из скобок 4

4(x+4+24)/(x+4) = 4*24/x

Сократим 4

(x+28)/(x+4) = 24/x

Перемножим крест-накрест

(x+28)x = 24(x+4)

x^2 + 28x = 24x + 96

x^2 + 4x - 96 = 0

D = 4 + 96 = 100

x = -2 +-10 = -12 или 8 

-12 не удовлетворяет, так как скорость не может быть минусовой. 

Значит скорость второго: 8 км/ч, он же и пришел к финишу на 4 часа позже первого, значит:

Ответ: 8км/ч

Answer 2

Problem Analysis

We are given that two cyclists simultaneously started a 96-kilometer race. The first cyclist traveled at a speed 4 km/h faster than the second cyclist and arrived at the finish line 4 hours earlier than the second cyclist. We need to find the speed of the cyclist who finished second.

Solution

Let's assume the speed of the second cyclist is x km/h. Then, the speed of the first cyclist would be x + 4 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 = 96 km - Speed = x + 4 km/h - Time = 96 / (x + 4) hours

For the second cyclist: - Distance = 96 km - Speed = x km/h - Time = 96 / x hours

According to the given information, the first cyclist arrived at the finish line 4 hours earlier than the second cyclist. Therefore, we can set up the equation:

96 / (x + 4) = 96 / x + 4

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

96x = 96(x + 4) + 4(x + 4)

Simplifying further:

96x = 96x + 384 + 4x + 16

Combining like terms:

96x - 96x - 4x = 384 + 16

Simplifying:

-4x = 400

Dividing both sides by -4:

x = -100

Since speed cannot be negative, we can ignore the negative solution. Therefore, the speed of the cyclist who finished second is 100 km/h.

Answer

The speed of the cyclist who finished second is 100 km/h.