# Rates

Students who are solid on rate problems will earn easy points on MathCounts!

The only formula to memorize is the definition of rate, $r=\frac{d}{t}$ where $d=$ distance and $t=$ time.  I find it helpful to draw a quick diagram so I can visualize what is happening to our MathCounts team on their way to and from the contest.  (H=home, MC = MathCounts contest.)

On the return trip we multiply the time by $2$, multiply the distance by $\frac{3}{2}$, and subtract $10$ mi/h from the rate.

The first equation I have written derives from the fact that the new rate is equal to the old rate minus 10 mi/h.  Then it is a matter of solving for $r=\frac{d}{t}$ which is the rate to the contest.

Source: MathCounts