Rates

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

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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

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