Tortoise A walks 52.0 feet per hour and tortoise B walks 12 inches per minute. Which tortoise travels faster? Explain.

Question

Use dimensional analysis to determine which rate is greater.

Answer 1

In order to compare the speeds of tortoise A and B, you need convert the units. The key to converting units is to multiply by the relevant ratios so that the units you don't want cancel and you are left with the units you do want. In this question, you want to know the relative speed of Tortoise A and Tortoise B, so it doesn't matter whether you convert A's units to B's or B's units to A's.

Coverting A's ft per hr into in per min.

52ft x 1hr x 12in = 52ft x 1hr x12in = 10.4in

1hr 60min 1ft 1hr x 60min x1ft min

Notice that you have both feet and hours in both the numerator and denominator. Anything divided by itself equal 1, so these units cancel out and you are left with 10.4in/min for A's speed. B is faster.

Answer 2

The tortoises rates of speed are in differing units. You have to convert one so it is the same as the other's .

Let's work with Tortoise B and convert its units to the same as those of tortoise A.

12 inches = 1 foot

60 minutes = 1 hour

Tortoise B walks 1 foot per minute and therefore 60 feet in an hour

Tortoise A walks 52 feet in 1 hour.

Tortoise B is faster.