Question

Каждые 15 мин автомобиль увеличивал свою скорость на 12 км/ч. За какое время он проехал 164 км, если первые 15 мин он двигался со скоростью 40 км/ч​.​​

Answer 1

Ответ:

2 ч или 120 мин

Объяснение:

15 мин = 1/4 часа

за первые 15 мин 40*(1/4)=10 км

40 +12 =52 новая скорость

52*(1/4)=13 км

разница 13-10=3 км

каждые 15 мин автомобиль проезжает на 3 км больше

арифметическая прогрессия

a1=10  d=3 cумма 164 найти n

(2a1+d(n-1))*n/2

(2*10+3(n-1))n/2=164

20n+3n^2-3n=328

3n^2+17n-328=0

n=(-17+√(289+3936)/6=(-17+65)/6=8

15*8=120 мин

Answer 2

Problem Analysis

We are given that a car increases its speed by 12 km/h every 15 minutes. We need to determine how long it takes for the car to travel a distance of 164 km, given that it initially moves at a speed of 40 km/h for the first 15 minutes.

Solution

To solve this problem, we can break it down into two parts: 1. Calculate the time it takes for the car to reach its maximum speed. 2. Calculate the time it takes for the car to travel the remaining distance at its maximum speed.

Let's calculate each part step by step.

Part 1: Time to reach maximum speed

The car increases its speed by 12 km/h every 15 minutes. Since the car initially moves at a speed of 40 km/h for the first 15 minutes, we need to calculate how many times the car increases its speed by 12 km/h.

To calculate the number of speed increases, we can use the following formula:

Number of speed increases = (Maximum speed - Initial speed) / Speed increase per 15 minutes

Given: - Initial speed = 40 km/h - Maximum speed = ? - Speed increase per 15 minutes = 12 km/h

Let's calculate the maximum speed:

Maximum speed = Initial speed + (Number of speed increases * Speed increase per 15 minutes)

Substituting the given values:

Maximum speed = 40 km/h + (Number of speed increases * 12 km/h)

To find the number of speed increases, we can use the formula:

Number of speed increases = (Maximum speed - Initial speed) / Speed increase per 15 minutes

Substituting the given values:

Number of speed increases = (Maximum speed - 40 km/h) / 12 km/h

Now, we need to find the maximum speed. To do this, we can substitute the value of the number of speed increases into the formula for the maximum speed:

Maximum speed = 40 km/h + ((Maximum speed - 40 km/h) / 12 km/h) * 12 km/h

Simplifying the equation:

Maximum speed = 40 km/h + Maximum speed - 40 km/h

Solving for the maximum speed:

Maximum speed = 40 km/h + Maximum speed - 40 km/h

Maximum speed = 2 * Maximum speed

Maximum speed = 80 km/h

Therefore, the maximum speed of the car is 80 km/h.

Part 2: Time to travel remaining distance at maximum speed

Now that we know the maximum speed of the car is 80 km/h, we can calculate the time it takes for the car to travel the remaining distance of 164 km at this speed.

To calculate the time, we can use the formula:

Time = Distance / Speed

Given: - Distance = 164 km - Speed = 80 km/h

Substituting the given values:

Time = 164 km / 80 km/h

Simplifying the equation:

Time = 2.05 hours

Therefore, it takes approximately 2.05 hours for the car to travel the remaining distance of 164 km at its maximum speed.

Total time

To calculate the total time, we need to add the time it takes for the car to reach its maximum speed (15 minutes) to the time it takes for the car to travel the remaining distance at its maximum speed (2.05 hours).

Total time = 15 minutes + 2.05 hours

Converting 15 minutes to hours:

Total time = 0.25 hours + 2.05 hours

Simplifying the equation:

Total time = 2.3 hours

Therefore, it takes approximately 2.3 hours for the car to travel a distance of 164 km, given that it initially moves at a speed of 40 km/h for the first 15 minutes and then increases its speed by 12 km/h every 15 minutes.

Answer

The car takes approximately 2.3 hours to travel a distance of 164 km, given that it initially moves at a speed of 40 km/h for the first 15 minutes and then increases its speed by 12 km/h every 15 minutes.