Question

Водитель Пётр должен был доехать до пункта назначения, находящегося на расстоянии 640 км, за 8 часов. Но у него не было с собой калькулятора, и он неправильно рассчитал нужную скорость. И, проехав 2 часа, он понял, что опаздывает. Поэтому Пётр увеличил скорость в 1,5 раза и ехал с этой скоростью следующие 4 часа. После этого он понял, что скорость слишком большая и её можно немного уменьшить. Поэтому он уменьшил скорость на 10 км/ч и оставшийся путь он преодолел ровно за 2 часа. Какую скорость водитель выбрал изначально?

Answer 1

S = 640 км = V₁*2 + 1.5V₁*4 + (1.5V₁-10)*2
640 = 2*V₁ + 6*V₁ + 3*V₁-20
660 = 2*V₁ + 6*V₁ + 3*V₁
660 = 11*V₁
V₁ = 60 км/ч

Answer 2

Initial Calculations and Speed Adjustment

The driver, Petr, was supposed to travel a distance of 640 km in 8 hours. However, after 2 hours of driving, he realized he was running late. He then increased his speed by 1.5 times and continued at this speed for the next 4 hours. Afterward, he realized that the speed was too high and reduced it by 10 km/h, and he covered the remaining distance in exactly 2 hours.

Calculating the Initial Speed

To find the initial speed of the driver, we can calculate the average speed for the entire journey and then work backward to find the initial speed.

The total time taken for the journey can be calculated as 2 hours (initial) + 4 hours (increased speed) + 2 hours (reduced speed) = 8 hours.

The total distance is 640 km.

Using the formula: Average Speed = Total Distance / Total Time

We can calculate the average speed and then find the initial speed.

Calculation

Average Speed = 640 km / 8 hours = 80 km/h.

The initial speed can be calculated using the time and distance covered at the initial speed.

Let's denote the initial speed as 'x' km/h. The time taken at the initial speed is 2 hours, and the distance covered at this speed is 2 hours * x km/h = 2x km.

The time taken at the increased speed is 4 hours, and the distance covered at this speed is 4 hours * 1.5x km/h = 6x km.

The remaining distance covered at the reduced speed is 640 km - (2x + 6x) km = 640 km - 8x km.

The time taken to cover the remaining distance at the reduced speed is 2 hours.

Using the above information, we can solve for the initial speed 'x'.

Solving for Initial Speed

2x + 6x + 640 - 8x = 640 8x - 8x + 640 = 640 640 = 640

This equation is true for any value of x, which means that the initial speed 'x' can be any value. Therefore, the initial speed chosen by the driver is indeterminate.

So, the initial speed chosen by the driver cannot be determined based on the given information.

If you have any further questions or need additional assistance, feel free to ask!