Question

Jethro used dimensional analysis to convert one rate of speed to another. Two of the conversion factors he used are 5280 ft/1 mi and 1 hr/60 min. What could be the units of the initial rate of speed and the final rate of speed? Justify your answer.

Answer 1

The units of the initial and final rates of speed are;

Initial rate of Speed = ft/hr

Final rate of speed = mi/min

• We are told that the conversion factors he used are;

5280 ft/1 mi and 1 hr/60 min

• Now, the meaning of 5280 ft/1 mi denotes that;

5280 ft mile is equivalent to 1 mile

This means that the initial distance unit used was ft while the final one was mile

Also, 1 hr/60 min denotes that;

1 hour is equivalent to 60 minutes.

This means that the initial time units used was hour while the final one was minute.

• In conclusion, since we know the initial time and distance units used, we can say that the initial rate of speed ft/hr while final speed rate was miles/minutes.

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