Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of $$ x $$ km till then, where $$ x $$ is a whole number and is palindromic (i.e., $$ x $$ remains unchanged when its digits are reversed). At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was:

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Accepted Answer

Let Brishti's average speed during the trip be $$ s $$ km/h. The total distance covered by Brishti after the trip is given as 26862 km. The distance covered during the trip in 8 hours is:  
$$
8s 	ext{ km}.
$$

The distance traveled before the trip, $$ x $$, is a palindrome, and it satisfies:  
$$
x = 26862 - 8s.
$$

Since both $$ x $$ and 26862 are palindromes, $$ x $$ must also be a palindromic number. To find the greatest possible average speed ($$ s $$), we test values of $$ s $$ such that:  
1. $$ s \leq 110 	ext{ km/h (maximum speed)} $$.  
2. The resulting value of $$ x = 26862 - 8s $$ is a palindrome.

Testing for values of $$ s $$ from the given options:  
- For $$ s = 100 	ext{ km/h} $$:  
$$
x = 26862 - (8 	imes 100) = 26862 - 800 = 26062.
$$  
This is a palindrome.

- For other values of $$ s $$ (e.g., 90 or 110), the resulting value of $$ x $$ is not a palindrome.

Thus, the **greatest possible average speed** at which Brishti drove during the trip is **100 km/h**.

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