Rates

Rate questions can usually be identified by the presence of mph, but any problem that involves the rate at which something is travelling or being done, is a rate questions.  Most rate questions can be solved using some form of the DIRT equation: \(Distance=Rate\times Time\).

Louise left her house and drove 12 miles to work. If she left at 2:00pm and arrived to work at 2:20pm, how fast was she travelling in miles per hour?

Strategy for \(\boldsymbol D\boldsymbol i\boldsymbol s\boldsymbol t\boldsymbol a\boldsymbol n\boldsymbol c\boldsymbol e\boldsymbol=\boldsymbol R\boldsymbol a\boldsymbol t\boldsymbol e\boldsymbol\times\boldsymbol T\boldsymbol i\boldsymbol m\boldsymbol e\):

  1. Write out \(\boldsymbol D\boldsymbol i\boldsymbol s\boldsymbol t\boldsymbol a\boldsymbol n\boldsymbol c\boldsymbol e\boldsymbol=\boldsymbol R\boldsymbol a\boldsymbol t\boldsymbol e\boldsymbol\times\boldsymbol T\boldsymbol i\boldsymbol m\boldsymbol e\) formula.
  2. Identify what you know. Does the problem tell you the distance? Does it tell you the time?
  3. Convert all values to proper units.  If the rate is in miles per hour, then the time must be in hours and the distance must be in miles.
  4. Plug values into the formula.
  5. Solve for the unknown variable.

A car is traveling 40 mph for 90 minutes, how far did the car travel in miles?

With rate questions, always work in consistent units.  Thus, we will first want to convert the 90 minutes into hours. Since 90 minutes would be 1.5 hours, our equation would be the following:

$$Distance=40\times1.5=60\;miles$$

Traps

Units!!
 
The SAT will sometimes give you values that first need to be converted. If given a value in seconds and a value in minutes, for example, convert all units to either seconds or minutes before completing the problem.
 
Travelling in segments
 
The SAT will occasionally split a trip into several segments (usually a beginning, middle, and an end). If they do this, each segment will have its own version of the \(Distance=Rate\times Time\) formula.