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

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006   kilo calorie

then ,802.3 kilo joule will be = 802.30.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.