I must not be too smart because I was dumb enough to take emode's IQ test. (actually, I think it was 'cuz I was bored). Anyway, I got this question wrong, and I can't understand why. What do you guys think is the answer? It seems ridiculously easy to me, yet they claim the answer to be something else. I'm wondering if I missed something. 20. In a race from point X to point Y and back, Jack averages 30 miles per hour to point Y and 10 miles per hour back to point X. Sandy averages 20 miles per hour in both directions. Between Jack and Sandy, who finished first? 1) Jack 2) Sandy 3) They tie 4) Neither 5) Impossible to tell
Distance from X to Y is Z Z miles*1 hour/30miles + Z miles * 1/10= 2/15 * Z hours Z miles *2 * 1hour/20 miles =1/10 Z hours 1/10 hours <2/15 hours
You are trying to average velocities on a per distance basis, but you can't do this because it takes longer to achieve the same distance at a slower speed. Thus, traveling at 10 miles/hour will need to weighted more than 30 miles/hour because Jack is at 10 miles/hour for a longer period of time than at 30. To average velocities, you have to do it on a per time basis.
Easier way to understand for my simpler mind: Suppose distance is 30 miles. J takes 1 hour there and 3 hour back for total of 4 hours S takes 1.5 hours each way for a total of 3 hours.
Duh.......it all looks so simple now. I won't forget that again. I felt so smart when they gave me the score, but this makes me feel so stupid.
To make this simpler, suppose X to Y is only 30 miles. Jack takes 1 hour from X to Y Jack takes 3 hours from Y to X total - 4 hours Sandy takes 1.5 hours from X to Y Sandy takes 1.5 hours from Y to X total - 3 hours Therefore the answer is Sandy *nevermind as already said*
Here's another way to look at it: On the first half of the race, Jack's speed is 1.5 times of Sandy's. On the second half, Sandy's speed is 2 times of Jack's.
This question didn't mention they are both going on a straight line, it's just an assumption we all make. (One can take the long route and one the short to get to a destination and back) Answer: 5) Impossible to tell
