Problem Solving

Hi AAPL,

We're told that Juan cycles at an average speed of 15 km/h, to the top of the hill (where the MIDPOINT of the trip is), then travels at an average speed of 20 km/h downhill. We're asked which of the following is the closest approximation of Juan's average speed, in kilometers per hour, 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):

Juan cycled 15 km/hour in one direction and then drove back (the same distance) at 20 km/hour. Driving the same distance at a faster speed takes LESS time, so Juan spent MORE time traveling 15 km/hour than he spent cycling 20 km/hour. This is ultimately a 'weighted average' - meaning that the average speed for the entire trip will be CLOSER to 15 than it is to 20. Looking at the Answers, we can immediately eliminate Answer C, D and E. Since the average speed has to be BETWEEN 15 and 20, we can also eliminate Answer A (it's clearly not between those numbers). There's only one answer left...

Final Answer: B

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

BTGmoderatorLU wrote:Juan goes out cycling outdoors. He travels at an average speed of 15km/h, to the top of the hill where the midpoint of the trip is. Going down hill, Juan travels at an average speed of 20km/h. Which of the following is the closest approximation of Juan's average speed, in kilometers per hour, for the round trip?

A. 15.0
B. 17.1
C. 17.5
D. 17.9
E. 20.0

We can let the one-way trip be 60 miles; therefore, we have:

Average Speed = (Total Distance)/(Total Time)

Average Speed = (60 + 60)/(60/15 + 60/20)

Average Speed = 120/7

Average Speed ≈ 17.1

Answer: B