January 2008 SAT Hard Math Question HELP #18

SATQuantum
Mon, 29 Jul 2013 02:43:59 +0000

The problem with the Harmonic mean formula is that it is only applicable to cases where the distance traveled in each segment is equal, and in addition we are given the average speed for each segment and asked to find the average speed for the entire journey. Students need to understand the origin of the formula, otherwise it is possible that they end up applying it to the wrong situations.

@muhammad9211 You are right that the formula would not work in this scenario. Instead, it is best to start with the definition of the average speed as the total distance divided by total time, and then compute the time for each segment and find the average speed. So far I have not seen anything on the Official SAT which has given this variation, but I won’t be surprised because it is well within the scope of SAT.