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A cyclist bikes at 12 miles per hour. Is the relationship between the distance and time a proportional relationship? Why or why not?

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1 Answer

Hi Aaron;
distance=(rate)(time)
distance=(12 m/h)(time)
The relationship between distance and time is proportional.
You asked why.  This is the reason...
The distance is in miles.  The time is in hours.
d miles=(12 miles/hour)(t hours)
Please note that on the right side of the equation, the unit of hours is in the denominator and numerator.  It cancels...
d miles=(12 miles/hour)(t hours)
d miles=(12 miles)(t)
The units on both sides are miles.  These cancel...
d miles=(12 miles)(t)
d=12t
The reason the two variables are proportional is because of the alignment of the units.