Problem Solving

Hi AAPL,

We're told that Gill drives 120 miles from Los Angeles to San Diego to fetch a package; on her way there she drives at 40 miles per hour and on her way back she drives 50% faster. We're asked for Gill's average velocity for the round trip. This question can be approached in a number of different ways. Here's how you can solve it with almost no math at all - just a little logic (and using the 'spread' of the Answer choices to your advantage):

Gill drove 40 miles/hour in one direction and then drove back (the same distance) at a speed that was 50% FASTER (40 mph + 20 mph = 60 miles/hour). Driving the same distance at a faster speed takes LESS time, so Gill spent MORE time traveling 40 miles/hour than she spent driving 60 miles/hour. This is ultimately a 'weighted average' - meaning that the average speed for the entire trip will be CLOSER to 40 than it is to 60. Looking at the Answers, we can immediately eliminate Answer C, D and E. Since the average speed has to be BETWEEN 40 and 60, we can also eliminate Answer A (it's clearly too small). There's only one answer left...

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity for the round trip?

A. 24 miles per hour
B. 48 miles per hour
C. 50 miles per hour
D. 53 1/3 miles per hour
E. 68 miles per hour

We can use the formula: average rate = total distance/total time.

The rate on the first leg is 40, and the rate on the second leg is 1.5 x 40 = 60.

The time on the first leg is 120/40 = 3, and the time on the second leg is 120/60 = 2.

The average speed is:

240/5 = 48

Answer: B