Question

Два автомобиля едут на встречу друг другу. Сейчас между ними 60 км. Скорость одного составляет 2/3 скорости другого. Найдите скорость каждого автомобиля, если известно, что они встретятся через 25 минут

Answer 1

25мин =5/12часа
60:5/12=60*12/5=144км/ч скорость сближения
1 + 2/3 =1 2/3=5/3
144:5/3=144*3/5=86,4км/ч скорость первого
144-86,4=57,6км/ч скорость второго

=====================
x -скорость одного
2/3x  -скорость второго
25мин=5/12ч

5/12*(x+2/3x)=60
5/12*1 2/3x=60
5/12*5/3x=60
25/36x=60
x=60*36/25
x=86,4км/ч скорость первого
86,4 * 2/3=28,8*2=57,6км/ч скорость второго

Answer 2

Problem Analysis

We are given that two cars are traveling towards each other, with a distance of 60 km between them. The speed of one car is 2/3 of the speed of the other car. We need to find the speed of each car, given that they will meet after 25 minutes.

Solution

Let's assume the speed of the slower car is x km/h. Therefore, the speed of the faster car will be (2/3)x km/h.

We know that speed is equal to distance divided by time. Since the cars will meet after 25 minutes, we can set up the following equation:

Distance = Speed × Time

For the slower car: 60 km = x km/h × (25/60) h For the faster car: 60 km = (2/3)x km/h × (25/60) h Now, we can solve these equations to find the speeds of the cars.

Calculation

Let's solve equation for the slower car:

60 km = x km/h × (25/60) h

Simplifying the equation: 60 km = (25/60) x km/h

Multiplying both sides by (60/25): 60 km × (60/25) = x km/h

Simplifying further: 144 km/h = x km/h

So, the speed of the slower car is 144 km/h.

Now, let's solve equation for the faster car:

60 km = (2/3)x km/h × (25/60) h

Simplifying the equation: 60 km = (25/60) (2/3)x km/h

Multiplying both sides by (60/25) and (3/2): 60 km × (60/25) × (3/2) = x km/h

Simplifying further: 216 km/h = x km/h

So, the speed of the faster car is 216 km/h.

Answer

Therefore, the speed of the slower car is 144 km/h and the speed of the faster car is 216 km/h.

Please let me know if you need any further assistance.