Find a recurrence relation for the number of ways to go n miles by foot walking at 2 miles per hour or jogging at 4 miles per hour or running at 8 miles per hour; at the end of each hour a choice is made of how to go the next hour. (b) how many ways are there to go 12 miles?

(a)

(b) 18 ways

Solution:

As per the question:

We need to find the no.of ways to go 'n' miles by foot:

From the question it is clear that, at each hours even miles can be traveled by a person, If the distance to be covered is odd, then there in no way 3 miles can be covered.

Thus defining recurrence as:

where

n: negative or odd

Then

(b) No. of ways to travel 12 miles:

Thus clearly there are 18 ways to travel 12 miles

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