Question

During a workout at the gym, you set the treadmill at a pase of 55.0 m/min. How many minutes will you walk if you cover a distance of 7500 ft?

Answer 1

Ok so there are several things going on here.
We're dealing with distance, rate and time. So we'll use the formula that connects them.
\[\large d=rt\]We want to solve for the time, in minutes, so we'll divide by sides by r,\[\large t=\dfrac{d}{r}\]

Answer 2

We'll also need a conversion for meters to feet.
Google is telling me that `1 meter = 3.28084 feet`.

So using this conversion factor, let's rewrite our \(r\) (rate) in terms of feet.\[\large r=\frac{55m}{\min}\]Multiplying by our conversion factor,\[\large r=\frac{55m}{\min}\left(\frac{3.28084\;ft}{m}\right)\]We can cancel out the meter units,\[\large r=\frac{55\cancel m}{\min}\left(\frac{3.28084\;ft}{\cancel m}\right)\]Giving us a rate in feet/min of,\[\large r=180.4462 \frac{ft}{\min}\]

Answer 3

\[\large d=7500 ft\]

Answer 4

Now we can plug in our pieces to solve for t (the total time traveled).\[\large t=\frac{7500ft}{180.4462\dfrac{ft}{\min}}\]