Question

1 hour = 3600 seconds and 1 mole = 5,280 feet. Make a conjecture about how you could convert a speed of 15 miles per hour to feet per second. Then convert

Answer 1

We know that speed (rate) is equal to distance over time.

The current unit of distance is miles, and we want to convert it to feet. The unit of time is hours, and we want seconds. In order to do this, we need to create a conversion factor.

Since $1 \ mi = 5,280 \ ft$ and $1 \ hr = 3,600 \ s$, we will use these are our conversion factors.

The goal in a dimensional analysis problem like this is for your units to work out. Remember, we want feet per second.

We write $speed = \dfrac{15 \ mi}{hr} * \dfrac{5,280 \ ft}{1 \ mi} * \dfrac{1 \ hr}{3,600 \ s} \\ \\ speed = \dfrac{22 \ ft}{s}$.

You may wonder why in the conversion factor, we chose to put feet over miles and hours over seconds. This is again because we want our units to cancel. If you have one unit the numerator and the same one in the denominator, the units cancel out.

In sum, the answer is 22 ft/s.