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 mile = 5280 feet
- 1 foot = 12 inches
- 1 inch = 2.54 centimeters
- 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:
-
Convert miles to feet: \[ 70 \text{ miles} \times 5280 \text{ feet/mile} \]
-
Convert feet to inches: \[ (\text{result from step 1}) \times 12 \text{ inches/foot} \]
-
Convert inches to centimeters: \[ (\text{result from step 2}) \times 2.54 \text{ cm/inch} \]
-
Convert hours to seconds: \[ (\text{result from step 3}) \div 3600 \text{ seconds/hour} \]
Now, let’s calculate it:
- \( 70 \times 5280 = 369600 \text{ feet/hr} \)
- \( 369600 \times 12 = 4435200 \text{ inches/hr} \)
- \( 4435200 \times 2.54 = 11215008 \text{ cm/hr} \)
- \( \frac{11215008}{3600} \approx 3114.86 \text{ cm/sec} \)
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.