Question

Два велосипедиста выехали одновременно навстречу друг другу из двух посёлков.Через 2 часа после выезда расстояние между ними стало равно 96 км.Какое расстояние между этими посёлками , если скорости велосипедистов 14км в час и 18 км в час?

Answer 1

14+18=32км/ч-общая скорость
96÷32+2=5ч-они ехали
32×5=160км

Answer 2

96/(14+18)=3-осталось проехать часов
3+2=5 -всего должны проехать
5х32=160
Ответ:160 километров

Answer 3

Problem Analysis

We have two cyclists who start simultaneously from two different villages and ride towards each other. After 2 hours, the distance between them is 96 km. We need to find the distance between the two villages given that the speeds of the cyclists are 14 km/h and 18 km/h.

Solution

Let's assume that the distance between the two villages is D km.

We can calculate the time it takes for the two cyclists to meet by dividing the distance between them (96 km) by the sum of their speeds (14 km/h + 18 km/h).

The time taken to meet is given by the formula:

Time = Distance / Speed

So, the time taken to meet is:

Time = 96 km / (14 km/h + 18 km/h)

Let's calculate the time taken to meet:

Time = 96 km / 32 km/h

Time = 3 hours

Since the cyclists started simultaneously and met after 2 hours, it means that they rode for 2 hours before meeting. Therefore, the remaining time to reach the meeting point is 1 hour.

Now, we can calculate the distance traveled by each cyclist in 2 hours:

Cyclist 1: Distance1 = Speed1 * Time = 14 km/h * 2 hours = 28 km

Cyclist 2: Distance2 = Speed2 * Time = 18 km/h * 2 hours = 36 km

After 2 hours, the distance between the two cyclists is 96 km. This distance is the sum of the distances traveled by each cyclist:

Distance1 + Distance2 = 96 km

28 km + 36 km = 96 km

64 km = 96 km

To find the distance between the two villages, we subtract the sum of the distances traveled by the cyclists from the total distance between them:

D = Total Distance - (Distance1 + Distance2)

D = 96 km - (28 km + 36 km)

D = 96 km - 64 km

D = 32 km

Therefore, the distance between the two villages is 32 km.

Answer

The distance between the two villages is 32 km.

Explanation

Two cyclists started simultaneously from two different villages and rode towards each other. After 2 hours, the distance between them became 96 km. Given that the speeds of the cyclists were 14 km/h and 18 km/h, we can calculate the distance between the two villages. By using the formula for time, we find that the time taken to meet was 3 hours. Since the cyclists met after 2 hours, they rode for 2 hours before meeting. Therefore, the remaining time to reach the meeting point is 1 hour. By calculating the distances traveled by each cyclist in 2 hours, we find that one cyclist traveled 28 km and the other traveled 36 km. Adding these distances gives a total of 64 km. Subtracting this total from the total distance between the cyclists (96 km) gives the distance between the two villages, which is 32 km.