Math CentralQuandaries & Queries


Question from Aaron, a student:

I can't do this math problem. please help.
Find 200m over 1 min times 60 min over 1 hr times 1 km over 1000 m.
the choices are a. 300 km/hr b. 12 km/hr c. 300 m/hr and d. 12 m/hr

Hi Aaron,

You have three fractions

\[\frac{200 \mbox{ m}}{1 \mbox{ min}} \times \frac{60 \mbox{ min}}{ 1 \mbox{ hr}} \times \frac{1 \mbox{ km}}{1000 \mbox{ m}}.\]

Since there are 60 minutes in an hour the middle fraction reduces to 1 with no units. The remaining numeric values reduce to $\large \frac15$ and the two units of metres cancel so you are left with

\[\frac15 \frac{\mbox{ km}}{\mbox{ min.}}\]

But the choices for answers have the units km/hr or m/hr. How do you convert km/min to km/hr or m/hr?


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