Happy Groundhog Day - The Solutions

February 4, 2008

This is solved by setting up a proportion but first we need to make sure that everything is in the same units. Since our answer is supposed to be in inches we’ll covert the measurements that are in feet to inches.

12 foot tree

 12 × 12 = 144 inches

15 foot shadow

            15 × 12 = 180 inches

Now we can set up the proportions.

144/180 = x/25

x = 20 inches

Since the population increases by the same factor every year, the population in 2007 is the geometric mean of the population at the beginning of 2006 and the population at the beginning of 2008.

2500/x = x/3025          

x2 = 7,562,500

x = 2750 groundhogs

We’ll solve this one by first drawing Henry’s route.

Now we can see that we can use Pythagorean’s Theorem to solve for the length of the dotted line.

            122 + (17 – 1)2 = x2

            144 + 256 = x2

            400 = x2

            x = 20 ft