Question

Use dimensional analysis to determine which rate is greater.

Tortoise A walks 71.0 feet per hour and tortoise B walks 12 inches per minute. Which tortoise travels faster? Complete the explanation.

Answer 1

Tortoise A: see below

Explanation:

Let's convert Tortoise B's rate of speed to feet per hour. To do so, we can use dimensional analysis and our knowledge of conversion rates.

• 
  `\displaystyle (12 \ in)/(1 \ min)`

Multiply this rate by 60 minutes per 1 hour.

• 
  `\displaystyle (12 \ in)/(1 \ min) * (60\ min)/(1\ hr)`

Multiply this rate by 1 foot per 12 inches.

• 
  `\displaystyle (12 \ in)/(1 \ min) * (60\ min)/(1\ hr) * (1 \ ft)/(12 \ in)`

By canceling out the units, we can see that ft/hr is left. This is our final answer's unit.

• 
  `\displaystyle (12 \ in)/(1 \ min) * (60\ min)/(1\ hr) * (1 \ ft)/(12 \ in) = \frac{720 \ ft} {12\ hr} = 60 \ (ft)/(hr)`

Tortoise B travels at a rate of 60 ft per hour, which is less than Tortoise A's speed, 71 ft per hour. Therefore, Tortoise A travels faster.