Question

Очень срочно! Два велосипедиста выехали навстречу друг другу, расстояние между ними 54 км, встретились через 2 часа. Какова скорость каждого, если расстояние , пройденное первым велосипедистом на 1.25 больше расстояния, пройденного вторым?

Answer 1

Пусть Х (км/ч) скорость одного, а 1,25х (км/ч) скорость другого.
Первый проехал до встречи 2х (км), а второй 2+1,25х=3,25х (км).
Вместе они проехали 54 км.
Составляем уравнение.
2х+3,25х=54
5,25х=54
х=10,29 км/ч скорость одного
10,29+3,25=13,54км/ ч скорость второго

Answer 2

Problem Analysis

We have two cyclists who start cycling towards each other. The distance between them is 54 km, and they meet after 2 hours. We need to find the speed of each cyclist given that the distance traveled by the first cyclist is 1.25 times greater than the distance traveled by the second cyclist.

Solution

Let's assume the speed of the first cyclist is x km/h and the speed of the second cyclist is y km/h.

We know that the distance traveled by the first cyclist is 1.25 times greater than the distance traveled by the second cyclist. Mathematically, we can represent this as:

Distance traveled by the first cyclist = 1.25 * Distance traveled by the second cyclist

We also know that the total distance between the two cyclists is 54 km, and they meet after 2 hours.

Using the formula Distance = Speed * Time, we can write two equations based on the given information:

Equation 1: Distance traveled by the first cyclist = x * 2

Equation 2: Distance traveled by the second cyclist = y * 2

From the given information, we also know that the distance traveled by the first cyclist is 1.25 times greater than the distance traveled by the second cyclist:

Equation 3: x * 2 = 1.25 * (y * 2)

Now, we can solve these equations to find the values of x and y.

Calculation

Let's solve the equations:

Equation 1: Distance traveled by the first cyclist = x * 2

Equation 2: Distance traveled by the second cyclist = y * 2

Equation 3: x * 2 = 1.25 * (y * 2)

From Equation 1, we can rewrite it as: x = (Distance traveled by the first cyclist) / 2

From Equation 2, we can rewrite it as: y = (Distance traveled by the second cyclist) / 2

Substituting the values of x and y in Equation 3, we get: (Distance traveled by the first cyclist) / 2 = 1.25 * ((Distance traveled by the second cyclist) / 2)

Simplifying the equation, we get: (Distance traveled by the first cyclist) = 1.25 * (Distance traveled by the second cyclist)

Since the total distance between the two cyclists is 54 km, we can rewrite the equation as: 54 = 1.25 * (Distance traveled by the second cyclist)

Simplifying further, we get: (Distance traveled by the second cyclist) = 54 / 1.25

Calculating the value, we find: (Distance traveled by the second cyclist) = 43.2 km

Now, we can substitute this value back into Equation 2 to find the speed of the second cyclist: y = (Distance traveled by the second cyclist) / 2 y = 43.2 / 2 y = 21.6 km/h

Finally, we can substitute the value of y into Equation 1 to find the speed of the first cyclist: x = (Distance traveled by the first cyclist) / 2 x = 54 / 2 x = 27 km/h

Answer

Therefore, the speed of the first cyclist is 27 km/h and the speed of the second cyclist is 21.6 km/h.