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×1000 m1 km×100 cm1 m=1,000,000 cm10 \text{ km} \times \dfrac{1000 \text{ m}}{1 \text{ km}} \times \dfrac{100 \text{ cm}}{1 \text{ m}} = 1,000,000 \text{ cm}

1,000,000 cm×1 quarter2.45 cm×$0.251 quarter=$102,040.816251,000,000 \text{ cm} \times \dfrac{1 \text{ quarter}}{2.45 \text{ cm}} \times \dfrac{\$0.25}{1 \text{ quarter}} = \$102,040.81625

Rounded to the nearest quarter, you would have $102,040.75 \$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.