Question

Ты-шофер грузовой машины. Скоро пост ГАИ. За превышение скорости по правилам полагается штраф. Спидометр не работает. Допустимая скорость 60 км/ч. Задачная формулировка: Счетчик грузовой машины показывал 12921 км. Через 2 ч на счетчике опять появилось число, которое читалось одинаково в обоих направлениях. С какой скоростью ехала эти 2 часа грузовая машина? Заплатишь ли ты штраф?

Answer 1

Штраф платить он не будет.проехал он 120 км со скоростью 55 км в час

Answer 2

Следующее число 13031, то есть 110 км проехал, скорость 55 км/ч, не платит штраф

Answer 3

Problem Analysis

To solve this problem, we need to determine the speed at which the truck was traveling for the given 2-hour period. We are given that the truck's odometer showed a reading of 12,921 km before the 2-hour period, and after the 2-hour period, a number appeared on the odometer that read the same forwards and backwards. We also know that the speed limit is 60 km/h and the speedometer is not working.

Solution

To find the speed at which the truck was traveling, we can use the formula:

Speed = Distance / Time

We know the distance traveled during the 2-hour period is the difference between the two odometer readings:

Distance = Odometer Reading after 2 hours - Odometer Reading before 2 hours

Let's calculate the distance traveled during the 2-hour period:

Distance = 12,921 km - Odometer Reading after 2 hours

Now, we need to find the Odometer Reading after 2 hours. Since the number on the odometer reads the same forwards and backwards, it must be a palindrome. We can start by checking the palindromic numbers that can be formed using the digits from 0 to 9.

Palindromic Numbers

A palindromic number is a number that reads the same forwards and backwards. For example, 121, 1221, and 12321 are palindromic numbers. We can check if a number is palindromic by comparing the digits from the left and right ends.

Let's list all the palindromic numbers that can be formed using the digits from 0 to 9:

- 00 - 11 - 22 - 33 - 44 - 55 - 66 - 77 - 88 - 99

Now, let's check if any of these palindromic numbers can be the Odometer Reading after 2 hours.

Checking the Odometer Reading

To check if a palindromic number can be the Odometer Reading after 2 hours, we need to calculate the distance traveled during the 2-hour period for each palindromic number and compare it with the distance calculated earlier.

Let's calculate the distance traveled for each palindromic number:

- For 00: Distance = 12,921 km - 12,900 km = 21 km - For 11: Distance = 12,921 km - 12,911 km = 10 km - For 22: Distance = 12,921 km - 12,922 km = -1 km (negative distance is not possible) - For 33: Distance = 12,921 km - 12,933 km = -12 km (negative distance is not possible) - For 44: Distance = 12,921 km - 12,944 km = -23 km (negative distance is not possible) - For 55: Distance = 12,921 km - 12,955 km = -34 km (negative distance is not possible) - For 66: Distance = 12,921 km - 12,966 km = -45 km (negative distance is not possible) - For 77: Distance = 12,921 km - 12,977 km = -56 km (negative distance is not possible) - For 88: Distance = 12,921 km - 12,988 km = -67 km (negative distance is not possible) - For 99: Distance = 12,921 km - 12,999 km = -78 km (negative distance is not possible)

From the calculations, we can see that only the palindromic number 00 results in a positive distance traveled during the 2-hour period. Therefore, the Odometer Reading after 2 hours is 12,900 km.

Now, let's calculate the speed using the formula:

Speed = Distance / Time

Speed = 21 km / 2 hours = 10.5 km/h

Since the speed limit is 60 km/h and the truck was traveling at a speed of 10.5 km/h, it was not exceeding the speed limit. Therefore, no fine is required.

Conclusion

The truck was traveling at a speed of 10.5 km/h for the 2-hour period, and no fine is required as it was not exceeding the speed limit.

Note: The above solution assumes that the odometer reading is accurate and there are no other factors affecting the distance calculation.