Eric hiked 10 miles in one day. How many feet is that per hour?

Question

I need to know the answer to this question. I’m confused on how to answer it .

Answer 1

Methi,

You want to convert the units. You probably know the conversions.

How many feet per mile?—5280

How many hours per day?—24

 

possibly your confusion is about HOW to use the conversions.

 

It may help to look at the units. You’re going to multiply or divide by these two fractions:

 

5280 feet

—————-

  1 mile

 

24 hours

————-

  1 day

 

we know Eric hiked

10 miles

———

 1 day

 

First, convert miles to feet, by multiplying the numerator by the conversion factor.

10 miles * 5280 feet

                —————

                 1 mile

———————————

     1 day

 

now look at the units (“mile”, “feet“, “day”). Notice that there are “miles” in both the numerator and denominator on top. That means that the UNITS themselves cancel each other out! That shows that we applied the conversion properly. This partial result is:

10 * 5280 feet

———————-

      1 day

 

So now let’s apply the hours per day conversion. Once again we will multiply the number of days by the number of hours. Only this time, it all happens in the denominator.

 

10 * 5280 feet

—————————-

1 day * 24 hours

             ——-—

               1 day

 

once again we are happy to see the DAYS cancel each other out, leaving:

 

10 * 5280 feet

———————

     24 hours

 

now just do the arithmetic, and you’re done.

 

This is a good reminder to keep track of measurement units, as it can give guidance as to how and where to do the conversions. (I am embarrassed to say my Answers rarely mention the units. I got stung on that a few weeks ago when the problem included both hours and minutes, and I failed to convert between them! I got an answer that was obviously clunky, and terribly wrong!)