# Rates

College.gov has your starting place for financial aid. One of the major concerns for prospective college students is money; college is expensive, and rising tuition costs combined with less government funding show no end in sight. However, there is money available to help students who need it, and the FAFSA is the best place to start.

## 4/15 Rates

Always remember to follow the Knowsys Method--even in your math classes. Thinking strategically and logically will help you be more efficient far beyond the SAT. First, read carefully to see what the question is actually asking. Then assess your options and select the best one. Attack the problem efficiently, then loop back to make sure that the answer you found matches the question that was originally asked.

A train traveling 60 miles per hour for 1 hour covers the same distance as a train traveling 30 miles per hour for how many hours?

First, note the bottom line.

train 2 hours= ?

Next, look back at the question to determine how you could solve it. You could determine the total distance traveled by train 1 and then calculate the time it would take train 2 to travel the same distance. You could also calculate the times relative to one another. That might sounds odd, but it is actually more efficient than the first method.

The first step is to set up a ratio of  the two rates given. Put the "new" rate, that of train 2, on top because it is the variable you are trying to find. Always reduce ratios to lowest terms.

$\frac{train 2}{train1}=\frac{30}{60}=\frac{1}{2}$

You now have a ratio of the two rates. Here's the cool part: simply flip it over to find a ratio of the two times.

If a car or train travels at twice the planned speed, the trip will take half as long as projected. If it travels at half the planned speed, the trip will take twice as long. This rule applies when traveling 2/3, 5/4, or any fraction of the original rate; the ratio of the times will be the reciprocal of that fraction.

$\frac{train2}{train1}=\frac{2}{1}$

This means that train 2 spent twice as much time as train 1 covering the same amount of ground.

train2 = 2(train1)

Since train 1 traveled for 1 hour, train 2 traveled for 2 hours. Loop back to make sure you answered the right question.

train 2 hours = 2

Good job! Now look at the answer choices.

A) 3

B) 2

C) 1

D) $\frac{1}{2}$

E) $\frac{1}{3}$