This is what I have is it right?

70 Miles / 1 Hr X 5280 feet / 1 Mile X 12 Inches / 1 Feet X 2.54 Cm/ 1 In X 1 M/ 100Cm X 1 Hr/60 sec

Is this right set up?

1 answer

To convert 70 miles per hour into centimeters per second, let's evaluate and correct your setup step by step.

Your setup looks like you're attempting to convert using the following relationships:

  1. 1 mile = 5280 feet
  2. 1 foot = 12 inches
  3. 1 inch = 2.54 centimeters
  4. 1 hour = 3600 seconds (not 60 seconds)

Given your expression:

\[ \frac{70 \text{ miles}}{1 \text{ hr}} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \times \frac{12 \text{ inches}}{1 \text{ foot}} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} \times \frac{1 \text{ hr}}{3600 \text{ sec}} \]

The corrected conversion factor for hours to seconds is crucial for obtaining the right result. Everything else looks great.

Now, let’s combine it step by step:

  1. Convert miles to feet: \[ 70 \text{ miles} \times 5280 \text{ feet/mile} \]

  2. Convert feet to inches: \[ (\text{result from step 1}) \times 12 \text{ inches/foot} \]

  3. Convert inches to centimeters: \[ (\text{result from step 2}) \times 2.54 \text{ cm/inch} \]

  4. Convert hours to seconds: \[ (\text{result from step 3}) \div 3600 \text{ seconds/hour} \]

Now, let’s calculate it:

  1. \( 70 \times 5280 = 369600 \text{ feet/hr} \)
  2. \( 369600 \times 12 = 4435200 \text{ inches/hr} \)
  3. \( 4435200 \times 2.54 = 11215008 \text{ cm/hr} \)
  4. \( \frac{11215008}{3600} \approx 3114.86 \text{ cm/sec} \)

So, your setup is almost correct, but you need to use 3600 seconds for the conversion from hours to seconds. The final result converts to approximately 3114.86 cm/second.