## 1170.91 – Path of Quarters

Assume for this problem that the diameter of a quarter is exactly 2.45 cm. (It actually is a bit smaller.) Imagine that the race course for a ten-kilometer race is marked out with a continuous path of quarters, each one touching the next. If you walked the entire ten kilometers and picked up all of the quarters, how much money would you have?

## Solution

This problem is best done using dimensional analysis:

$10 km \times \frac{1000m}{1km} \times \frac{100cm}{1m} = 1,000,000cm,$

$1,000,000cm \times \frac{1quarter}{2.45cm} \times \frac{\$0.25}{1quarter} = \$102,040.81625.$

Rounded to the nearest quarter, you would have \102,040.75$. This many quarters would weigh over 5,000 pounds and take up over 350 gallons, so all things considered, this is not a viable strategy for making money.