Question

На поездку из города А в город Б автомобиль затратил 1 час.Возвращаясь обратно,он увеличил скорость на 14,4 км/ч,и поездка заняла у него на 10 минут меньше,чем из А в Б.сколько километров составляет путь от города А до города Б? ВАРИАНТЫ:58км;60км;14.4км;72км.

Answer 1

S=vt s=(v+14,4)*50 s=v*60 приравнивая получим , что 50v+720=60v
10v=720
v=72 , но это скорость только , а если расстояние , то 4320

Answer 2

Problem Analysis

We are given that a car took 1 hour to travel from city A to city B. On the return journey, the car increased its speed by 14.4 km/h and the trip took 10 minutes less than the journey from A to B. We need to determine the distance between city A and city B.

Solution

Let's assume the distance between city A and city B is d kilometers.

From the given information, we can set up the following equations:

Equation 1: Time taken from A to B = 1 hour = 60 minutes Equation 2: Time taken from B to A = Time taken from A to B - 10 minutes

Using the formula distance = speed × time, we can write the following equations:

Equation 3: d = speed from A to B × time from A to B Equation 4: d = speed from B to A × time from B to A

Let's solve these equations to find the distance between city A and city B.

Solution Steps

Step 1: Convert the time taken from A to B to minutes: 1 hour = 60 minutes. Step 2: Convert the time taken from B to A to minutes: Time from A to B - 10 minutes. Step 3: Substitute the values into equations 3 and 4. Step 4: Solve the equations to find the value of d, which represents the distance between city A and city B.

Calculation

Step 1: Convert the time taken from A to B to minutes: 1 hour = 60 minutes. Step 2: Convert the time taken from B to A to minutes: 60 minutes - 10 minutes = 50 minutes.

Substituting the values into equations 3 and 4:

Equation 3: d = speed from A to B × 60 minutes Equation 4: d = speed from B to A × 50 minutes

Since the car increased its speed by 14.4 km/h on the return journey, the speed from B to A is greater than the speed from A to B by 14.4 km/h.

Let's assume the speed from A to B is s km/h. Therefore, the speed from B to A is s + 14.4 km/h.

Substituting the values into equations 3 and 4:

Equation 3: d = s × 60 minutes Equation 4: d = (s + 14.4) × 50 minutes

Since both equations are equal to d, we can set them equal to each other:

s × 60 = (s + 14.4) × 50

Simplifying the equation:

60s = 50s + 720

10s = 720

s = 72

Now we can substitute the value of s into equation 3 to find the distance d:

d = 72 × 60

d = 4320 km

Answer

Therefore, the distance between city A and city B is 4320 km.