A train traveled at a constant rate of $f$ feet per second. How many feet did it travel in $x$ minutes? I know the correct answer is (D), however, I don't understand why (D) is correct. Can someone explain it to me; I struggle with math?

 A: There are sixty seconds in a minute, so to convert $x$ minutes to seconds, we must multiply by 60 to get $60x$.  Now, we're given that the train is traveling at a constant speed of $f$ feet per second.  Thus, by multiplying by the number of seconds, we will know how many feet the train has gone, which is $60xf=60fx$.
A: The first step is to write out any relationships given. In this case, the train traveled at a constant rate, or speed of $f$ ft./s. So our relationship would be
$$f=\frac{\Delta d}{\Delta t}$$
where $\Delta d$ is the change in distance in feet, and $\Delta t$ is the change in time measured in seconds. Solving for the change in distance we have
$$\Delta d=f\Delta t$$
It looks easy, but we are given time in minutes, not seconds, so we need to multiply by a conversion factor as follows
$$\Delta d=f \frac{ft}{s}\cdot x\:min\cdot\frac{60\:s}{1\:min}$$
which may be easier to read if I express it like this
$$\Delta d=\frac{f\:ft}{1\:s}\cdot \frac{x\:min}{1}\cdot\frac{60\:s}{1\:min}$$
Notice how the units cancel giving us
$$\Delta d=60fx\:min.$$
I call this method chaining, and it makes conversions really easy. I just wanted to complete a couple more direct examples before finishing my post. Suppose we wish to calculate the number of seconds in a three dozen years.
$$3\text{ dozen years}\cdot\frac{12\text{ years}}{1\text{ dozen year}}\cdot\frac{365.24\text{ days}}{1\text{ year}}\cdot\frac{24\text{ hours}}{1\text{ day}}\cdot\frac{60\text{ minutes}}{1\text{ hour}}\cdot\frac{60\text{ seconds}}{1\text{ minute}}$$
Notice how all of the units cancel out except for $seconds$, giving us
$$(3)(12)(365.24)(24)(60)(60)\text{ seconds}=1136042496\text{ seconds}$$
Finally, consider a conversion ratio that doesn't have 1 as a denominator. Suppose that 3 miles is approximately 5 kilometers. Convert 25 miles to kilometers.
$$25\text{ mi.}\cdot\frac{5\text{ km}}{3\text{ mi.}} = \frac{25\cdot5}{3}\text{ km}\approx41.7\text{ km}$$
Read $\displaystyle\frac{5\text{ km}}{3\text{ mi.}}$ as 5 kilometers per 3 miles.
