Question

Расстояние между двумя пунктами равна 54 км. Из этих пунктов одновременно навстречу друг другу выехали два велосипедиста. Через 2 ч они встретились. До встречи расстояние, преодоленное первым велосипедиста,оказалось в 1,25 раз больше,чем расстояние , преодоленное вторым велосипедистом. Найдите скорость первого велосипедиста, второго велосипедиста. ПОМОГИТЕ ПОЖАЛУЙСТА ДОБРЫЕ ЛЮДИ!

Answer 1

1) Пусть второй велосипедист преодолел $x$ км. Тогда первый велосипедист преодолел $1,25x$. Зная, что расстояние между пунктами 54 км, составим уравнение.
$x+1,25x=54$
$2,25x=54$
$x= \frac{54}{2,25}$
$x=24$
Значит второй велосипедист преодолел 24 км.
2)  $24:2=12$ км/ч - скорость второго велосипедиста
3) $24*1,25=30$ км - преодолел первый велосипедист
4) $30:2=15$ км/ч - скорость первого велосипедиста
Ответ: 15 км/ч, 12 км/ч

Answer 2

Problem Analysis

We are given that the distance between two points is 54 km. Two cyclists start simultaneously from these points and meet after 2 hours. The distance covered by the first cyclist is 1.25 times greater than the distance covered by the second cyclist. We need to find the speeds of both cyclists.

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 covered by the first cyclist is 1.25 times greater than the distance covered by the second cyclist. Therefore, we can write the equation:

1.25y = x

We also know that the total distance covered by both cyclists is 54 km. Since they meet after 2 hours, we can write the equation:

2x + 2y = 54

Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Let's solve the system of equations:

1.25y = x (Equation 1) 2x + 2y = 54 (Equation 2)

To solve this system, we can use the substitution method. Rearrange Equation 1 to solve for x:

x = 1.25y (Equation 3)

Substitute Equation 3 into Equation 2:

2(1.25y) + 2y = 54

Simplify:

2.5y + 2y = 54

Combine like terms:

4.5y = 54

Divide both sides by 4.5:

y = 12

Substitute the value of y back into Equation 3 to find x:

x = 1.25(12) = 15

Therefore, the speed of the first cyclist is 15 km/h and the speed of the second cyclist is 12 km/h.

Answer

The speed of the first cyclist is 15 km/h and the speed of the second cyclist is 12 km/h.