The user-friendly version of this content is available here.
The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.
This problem trains for: SAT-I, AMC-8, GMAT.
Three buses serve a loop-shaped line with a total length of 12 miles. Assuming that the buses are equally spaced and run at the same average speed of 48 miles per hour, what is the probability for a passenger who shows up at a random time at a bus station to get on a bus during the first five minutes of waiting?
Each bus needs 5 minutes to transit from one station to the next. This is because there are 4 miles between two adjacent station. Since the bus travels 48 miles in 60 minutes, it will travel 4 miles in 5 minutes (distance-time are directly proportional quantities).
Therefore, for a passenger showing up at a random time at a station, the probability of getting on a bus in the first 5 minutes of waiting is 1 (this is a certain event).