Math CentralQuandaries & Queries


Question from ron, a parent:

if a vehicle travels 50 feet in 2.5 seconds what is the speed in mph.
3600 sec in hour /5280 feet in a mile i get .68181818. how do i figure the 2.5
seconds. all the calculators I've used show 34 mph is that correct or am i forgetting the 2.5 second. please help.

Hi Ron,

The units give the key here. You divided 3600 by 5280 to get 0.68181818 and the units are

\[\frac{\mbox{sec}}{\mbox{hr}}\times \frac{\mbox{miles}}{\mbox{feet}}.\]

To get 34 you multiplied 0.68181818 by 50 so the units now are

\[\frac{\mbox{sec}}{\mbox{hr}}\times \frac{\mbox{miles}}{\mbox{feet}}\times \mbox{feet}\]

which simplifies to

\[\frac{\mbox{sec}\times \mbox{miles}}{hr}.\]

But you want miles per hour.

I would let the units guide me from the start. the vehicle travels 50 feet in 2.5 seconds so that's

\[\frac{50}{2.5} \frac{\mbox{feet}}{\mbox{sec}}.\]

To convert to miles per hour you need

\[\frac{50}{2.5} \frac{\mbox{feet}}{\mbox{sec}} \times \frac{\mbox{__?__}}{\mbox{__?__}} \frac{\mbox{sec}}{\mbox{hr}}\times\frac{\mbox{__?__}}{\mbox{__?__}}\frac{\mbox{miles}}{\mbox{feet}}.\]

You know that there are 3600 seconds in an hour and 5280 feet in a mile so the above simplifies to

\[\frac{50}{2.5} \times \frac{3600}{1} \times\frac{1}{5280}\frac{\mbox{miles}}{\mbox{hr}}.\]


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