Question

Из пункта А в пункт Б, расстояние между которами 18 км, одновременно выезжают два мотоциклиста. Скорость одного из них на 4 км/ч меньше скорости другого. Велосипедист, который первым прибыл в Б, сразу же повернул обратно и встретил другого влосипедиста через 1ч.30мин. после выезда из А. На каком расстоянии от пункта Б произошла встреча?

Answer 1

1час30минут = 1,5часа

пусть:

х - скорость первого

х + 4 - скорость второго

у - искомое расстояние

составим систему:

1,5х = 18-у

1,5(х+4) = 18+у ---> 1,5х - у = 12 (то же уравнение после раскрытия скобок и упрощения)

из первого уравнения:

у = 18 - 1,5х

подставим во второе:

1,5х - (18 - 1,5х) = 12

1,5х - 18 + 1,5х = 12

3х = 30

х = 10 (км/ч - скорость первого, т.е. скорость второго 14 км/ч)

подставляем в первое:

1,5 * 10 = 18 - у

15 = 18 - у

у = 18 - 15

у = 3

Ответ: встреча произошла на расстоянии 3 км от пункта Б

_______________

проверим:

10 * 1,5 = 15 км - проехал первый (не доехал 3 км до Б)

14 * 1,5 = 21 км - проехал второй (доехал до Б, развернулся и проехал еще 3 км от Б)

Answer 2

Problem Analysis

We have two motorcyclists traveling from point A to point B, with a distance of 18 km between them. The speed of one motorcyclist is 4 km/h less than the speed of the other. The first cyclist arrives at point B, immediately turns back, and meets the second cyclist 1 hour and 30 minutes after leaving point A. We need to determine the distance from point B where the meeting occurred.

Solution

Let's assume the speed of the faster motorcyclist is x km/h. Then the speed of the slower motorcyclist is x - 4 km/h.

We can calculate the time it takes for the first cyclist to reach point B using the formula:

time = distance / speed

The time taken by the first cyclist to reach point B is:

time1 = 18 / x

After reaching point B, the first cyclist immediately turns back and meets the second cyclist 1 hour and 30 minutes (1.5 hours) later. So, the time taken by the second cyclist to reach the meeting point is:

time2 = 1.5 hours

The distance traveled by the second cyclist in 1.5 hours is:

distance2 = (x - 4) * 1.5

Since the distance traveled by the first cyclist is the same as the distance traveled by the second cyclist, we can equate the two distances:

18 = (x - 4) * 1.5

Simplifying the equation:

18 = 1.5x - 6

1.5x = 24

x = 16

The speed of the faster motorcyclist is 16 km/h. Therefore, the speed of the slower motorcyclist is 16 - 4 = 12 km/h.

To find the distance from point B where the meeting occurred, we can substitute the value of x into the equation for distance2:

distance2 = (16 - 4) * 1.5 = 12 * 1.5 = 18 km

Therefore, the meeting occurred at a distance of 18 km from point B.

Answer

The meeting between the two motorcyclists occurred at a distance of 18 km from point B.