Students who are solid on rate problems will earn easy points on MathCounts!
The only formula to memorize is the definition of rate, where distance and 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 , multiply the distance by , and subtract 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 which is the rate to the contest.