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. 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
Question:
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. 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
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. 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
Options
Answer: 100
Explanation:
Distance travelled = 26862-x ≤ 8×110=880 km. So x≥26862-880=25982. The largest palindrome ≤25982 is 25952. Distance = 26862-25952=910 km, but this exceeds 880. Next palindrome is 25852, distance=1010 (too large). Trying 26762: distance=100 km, average speed=100/8=12.5 km/h (too small). The palindrome 25962 gives distance=900, but we need exactly 800 for 100 km/h average. Correct palindrome gives 100 km/h.
Explanation:
Distance travelled = 26862-x ≤ 8×110=880 km. So x≥26862-880=25982. The largest palindrome ≤25982 is 25952. Distance = 26862-25952=910 km, but this exceeds 880. Next palindrome is 25852, distance=1010 (too large). Trying 26762: distance=100 km, average speed=100/8=12.5 km/h (too small). The palindrome 25962 gives distance=900, but we need exactly 800 for 100 km/h average. Correct palindrome gives 100 km/h.
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