Question

ДВЕ ДЕВОЧКИ ОДНОВРЕМЕННО ПОБЕЖАЛИ НАВСТРЕЧУ ДРУГ ДРУГУ ПОСПОРТИВНОЙ ДОРОЖКЕ, ДЛИНА КОТОРОЙ 420 М . КОГДА ОНИ ВСТРЕТИЛИСЬ, ПЕРВАЯ ПРОБЕЖАЛА НА 60 М БОЛЬШЕ, ЧЕМ ВТОРАЯ. С КАКОЙ СКОРОСТЬЮ БЕЖАЛА КАЖДАЯ ДЕВОЧКА, ЕСЛИ ОНИ ВТРЕТИЛИСЬ ЧЕРЕЗ 30 СЕК.

Answer 1

Х- пробежала вторая девочка
х+60 -пробежала первая
х+х+60=420
2х=420-60
2х=360
х=360:2
х=180 м - вторая девочка
180+60=240 м первая девочка
180:30=6 м\с скорость второй девочки
240:30=8 м\с скорость первой

или
420-60=360м
360:2=180 м бежала до встречи вторая девочка
180+60=240 м бежала до встречи первая девочка
180:30=6 м\с ск. второй
240:30=8 м\с ск. первой

Answer 2

Problem Analysis

We are given that two girls are running towards each other on a sports track. The length of the track is 420 meters. When they meet, the first girl has run 60 meters more than the second girl. We need to determine the speed at which each girl is running.

Solution

Let's assume that the speed of the first girl is x meters per second and the speed of the second girl is y meters per second.

We know that the total distance covered by both girls is equal to the length of the track, which is 420 meters. So we can write the equation:

Distance covered by the first girl + Distance covered by the second girl = Total distance

Using the formula Distance = Speed × Time, we can rewrite the equation as:

(x × t) + (y × t) = 420

We are also given that when they meet, the first girl has run 60 meters more than the second girl. So we can write another equation:

Distance covered by the first girl - Distance covered by the second girl = 60

Using the formula Distance = Speed × Time, we can rewrite the equation as:

(x × t) - (y × t) = 60

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

Solution Steps

1. Solve the system of equations: - (x × t) + (y × t) = 420 - (x × t) - (y × t) = 60

2. Add the two equations together to eliminate the t variable: - 2(x × t) = 480

3. Solve for x × t: - x × t = 240

4. Divide both sides of the equation by t to solve for x: - x = 240 / t

5. Substitute the value of x into one of the original equations to solve for y: - (240 / t) × t - (y × t) = 60 - 240 - y × t = 60 - y × t = 240 - 60 - y × t = 180 - y = 180 / t

6. We are given that they meet after 30 seconds, so substitute t = 30 into the equations to find the values of x and y: - x = 240 / 30 = 8 - y = 180 / 30 = 6

Answer

The first girl is running at a speed of 8 meters per second, and the second girl is running at a speed of 6 meters per second.