Final answer:
The motorcyclist will cross the 400-mile mark in the 65th hour of driving.
Step-by-step explanation:
To find the hour of driving when the motorcyclist crosses the 400-mile mark, we need to determine the pattern of the distances covered in each hour. The motorcyclist drives 10 miles in the first hour and in each subsequent hour, drives 6 miles more than the previous hour.
Let's represent the total distance covered after each hour as a sequence:
1st hour: 10 miles
2nd hour: 10 + 6 = 16 miles
3rd hour: 16 + 6 = 22 miles
4th hour: 22 + 6 = 28 miles
...
We can see that for each hour, the distance increases by 6 miles. So, the pattern can be represented by the formula: distance = 10 + 6n, where n is the number of hours.
To find the hour when the motorcyclist crosses the 400-mile mark, we can set up the equation:
10 + 6n = 400
Solving for n:
6n = 400 - 10
6n = 390
n = 65
Therefore, the motorcyclist will cross the 400-mile mark in the 65th hour of driving.