Question

Три мотоциклиста стартуют одновременно из одной точки кольцевого шоссе в одном направлении. Первый мотоциклист впервые догнал второго, сделав 4,5 круга после старта, а за 0,5 ч до этого он впервые догнал третьего мотоциклиста. Второй мотоциклист впервые догнал третьего через 3 ч после старта. Сколько кругов в час делает первый мотоциклист?

Answer 1

(9/2)S/V1=S/(V1-V2) 
((9/2)S/V1)-1/2=S/(V1-V3) 
S/(V2-V3)=3 
введите новые переменные S/V1=x 
S/V2=y 
S/V3=z 
ТЕБЕ НАДО НАЙТИ ТОЛЬКО X!!! 
9/2x=1/(x-y) 
9/2x-1/2=1/(x-z)(2) 
1/(y-z)=3 
(2/9)x=x-y 
y=(7/9)x 
Z=(7/9)x-1/3 
подставишь во 2, получишь квадратное уравнение , найдешь x 

Answer 2

Problem Analysis

We are given the information about three motorcyclists starting simultaneously from the same point on a circular highway. We need to determine how many laps the first motorcyclist completes in an hour.

Solution

Let's analyze the given information step by step to find the solution.

1. The first motorcyclist overtakes the second motorcyclist after completing 4.5 laps from the start. This means that the first motorcyclist completes 4.5 laps in the time it takes the second motorcyclist to complete 0.5 laps. 2. The first motorcyclist overtakes the third motorcyclist 0.5 hours before overtaking the second motorcyclist. 3. The second motorcyclist overtakes the third motorcyclist 3 hours after the start.

To find the number of laps the first motorcyclist completes in an hour, we need to determine the time it takes for the first motorcyclist to complete one lap.

Let's assume: - The time taken by the first motorcyclist to complete one lap is x hours.

Using the given information, we can create the following equations:

Equation 1: The first motorcyclist completes 4.5 laps in the time it takes the second motorcyclist to complete 0.5 laps. Equation 2: The first motorcyclist overtakes the third motorcyclist 0.5 hours before overtaking the second motorcyclist. Equation 3: The second motorcyclist overtakes the third motorcyclist 3 hours after the start.

Let's solve these equations to find the value of x.

Equation 1:

The first motorcyclist completes 4.5 laps in the time it takes the second motorcyclist to complete 0.5 laps.

The ratio of laps completed by the first motorcyclist to the second motorcyclist is equal to the ratio of time taken by the first motorcyclist to the second motorcyclist.

Therefore, we can write:

4.5 / 0.5 = x / 1

Simplifying the equation:

9 = x

So, the first motorcyclist takes 9 hours to complete one lap.

Equation 2:

The first motorcyclist overtakes the third motorcyclist 0.5 hours before overtaking the second motorcyclist.

This means that the time taken by the first motorcyclist to complete one lap is equal to the time taken by the third motorcyclist to complete 0.5 laps.

Therefore, we can write:

x = 0.5 / 0.5

Simplifying the equation:

x = 1

So, the first motorcyclist takes 1 hour to complete one lap.

Equation 3:

The second motorcyclist overtakes the third motorcyclist 3 hours after the start.

This means that the time taken by the second motorcyclist to complete one lap is equal to the time taken by the third motorcyclist to complete 3 laps.

Therefore, we can write:

1 / 3 = 1 / y

Simplifying the equation:

y = 3

So, the third motorcyclist takes 3 hours to complete one lap.

Conclusion

From the above analysis, we have determined the following: - The first motorcyclist takes 1 hour to complete one lap. - The second motorcyclist takes 3 hours to complete one lap. - The third motorcyclist takes 3 hours to complete one lap.

To find the number of laps the first motorcyclist completes in an hour, we divide the time taken by the first motorcyclist to complete one lap by 1 hour:

1 / 1 = 1

Therefore, the first motorcyclist completes 1 lap in an hour.

Answer

The first motorcyclist completes 1 lap in an hour.

Note: The solution is based on the given information and the assumptions made.