Question

Из пунктов A и B одновременно навстречу друг другу выехали два велосипедиста встретились через 2 часа. С какой средней скоростью ехал каждый велосипедист если один из них проезжал за час на 3 км больше другого, а расстояние между A и B 42 км (по действиям)

Answer 1

Ответ: 9 км/ч ; 12 км/ч

Пошаговое объяснение:

х - скорость 1

х + 3 - скорость 2

(х + х + 3)2 = 42

4х + 6 = 42

4х = 36

х = 9 км/ч - скорость 1

9 + 3 = 12 км/ч - скорость 2

Answer 2

Problem Analysis

Two cyclists start simultaneously from points A and B and meet after 2 hours. The distance between A and B is 42 km. One of the cyclists travels 3 km more than the other in one hour. We need to find the average speed of each 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. Since the first cyclist travels 3 km more than the second cyclist in one hour, we can write the following equation:

x = y + 3 We know that the distance traveled by each cyclist can be calculated using the formula distance = speed × time. Since both cyclists meet after 2 hours, we can write the following equations:

x × 2 = distance from A to meeting point y × 2 = distance from B to meeting point We also know that the sum of the distances traveled by both cyclists is equal to the total distance between A and B:

distance from A to meeting point + distance from B to meeting point = 42 km Now, let's solve the equations to find the values of x and y.

From equation we can rewrite it as:

distance from A to meeting point = x × 2

From equation we can rewrite it as:

distance from B to meeting point = y × 2

Substituting these values into equation we get:

x × 2 + y × 2 = 42

Simplifying the equation, we have:

2x + 2y = 42

Dividing both sides of the equation by 2, we get:

x + y = 21 Now, we have two equations: equation and equation We can solve these equations simultaneously to find the values of x and y.

Substituting the value of x from equation into equation we get:

(y + 3) + y = 21

Simplifying the equation, we have:

2y + 3 = 21

Subtracting 3 from both sides of the equation, we get:

2y = 18

Dividing both sides of the equation by 2, we get:

y = 9

Substituting the value of y into equation we get:

x = 9 + 3

Simplifying the equation, we have:

x = 12

Therefore, the first cyclist traveled at an average speed of 12 km/h, and the second cyclist traveled at an average speed of 9 km/h.

Answer

The first cyclist traveled at an average speed of 12 km/h, and the second cyclist traveled at an average speed of 9 km/h.

Explanation

The first cyclist traveled at a speed of 12 km/h, covering a distance of 24 km in 2 hours. The second cyclist traveled at a speed of 9 km/h, covering a distance of 18 km in 2 hours. The sum of their distances is equal to the total distance between A and B, which is 42 km.

Therefore, the solution is consistent with the given information.