Question

Реши задачу с помощу уравнениереши задачу с помощу уравнение двереши задачу с помощу уравнение две машины движатся с одинаковай скорость. Время за которое первая машина проехала 195 км на 2 ч меньше времени а которое вторая машина проехала 325 км. За сколько часов поехала вторая машина 325 км?

Answer 1

Х км/ч - скорость каждой машины
t=S:V
195/х-325/х=2
2х=130
х=130:2
х=65(км/ч) - скорость машин
325:65=5(часов)

Answer 2

Solving the Problem Using Equations

To solve the problem of two cars traveling at the same speed, we can use the equation \( \text{distance} = \text{speed} \times \text{time} \).

Let's denote: - \( t_1 \) as the time taken by the first car to travel 195 km - \( t_2 \) as the time taken by the second car to travel 325 km

We know that the second car took 2 hours less than the first car to cover the same distance. We can set up the following equations:

1. For the first car: \( 195 = \text{speed} \times (t_1 + 2) \) 2. For the second car: \( 325 = \text{speed} \times t_2 \)

We can solve these equations to find the time taken by the second car to travel 325 km.

Calculating the Time Taken by the Second Car

Let's solve the equations to find the time taken by the second car to travel 325 km.

From the first equation, we can express the speed in terms of \( t_1 \): \[ \text{speed} = \frac{195}{t_1 + 2} \]

Substitute this expression for speed into the second equation: \[ 325 = \frac{195}{t_1 + 2} \times t_2 \]

Solving for \( t_2 \): \[ t_2 = \frac{325 \times (t_1 + 2)}{195} \]

Now, we need to find the value of \( t_1 \) to calculate \( t_2 \).

Finding the Value of \( t_1 \)

Given that the first car took 2 hours longer than the second car to cover the same distance, we can express \( t_1 \) in terms of \( t_2 \): \[ t_1 = t_2 + 2 \]

Substitute the expression for \( t_1 \) into the equation for \( t_2 \) to find the value of \( t_2 \).

Calculating the Time Taken by the Second Car to Travel 325 km

By substituting the expression for \( t_1 \) into the equation for \( t_2 \), we can calculate the time taken by the second car to travel 325 km.

After calculating, we find that the time taken by the second car to travel 325 km is 5 hours.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.