To solve this problem, we can set up a proportion to find the ratio between the person's usual time and the time it took when walking at 5/6 of their usual rate.
Let's say the person's usual time is represented by "x" minutes.
According to the problem, when the person walks at 5/6 of their usual rate, they are 40 minutes late. This means that the time it took them to complete the journey at this slower rate was the usual time plus 40 minutes.
Setting up the proportion:
$\frac{x}{\text{usual rate}} = \frac{x+40}{\text{slower rate}}$
Since the person is walking at 5/6 of their usual rate, the slower rate is 5/6 of the usual rate.
$\frac{x}{\text{usual rate}} = \frac{x+40}{\frac{5}{6}\text{usual rate}}$
To simplify the equation, we can multiply both sides by the usual rate:
$x = \frac{x+40}{\frac{5}{6}}$
Now, we can solve for x by cross-multiplying:
$6x = 5(x+40)$
$6x = 5x + 200$
$x = 200$
Therefore, the person's usual time is 200 minutes.
To convert this to hours and minutes, we divide 200 by 60:
200 minutes รท 60 = 3 hours 20 minutes.
Therefore, the correct answer is C) 3 hours 20 minutes.