A certain road goes up one side of a hill and back down the other side. Each of the two segments is one mile long. If I drive my car up the hill at a constant speed of 30 mph, how fast must I drive the downhill segment to average 60 mph for the entire trip? Hint: If you did this in your head, you're probably wrong.
Well logically: (30+x)/2=60 30+x=120 x=90 so 90 MPH, but I did do that in my head, so it is probably wrong, can we have a hint
The time for a 2-mile trip at 60 MPH is 2 minutes. When you get to the top of the hill at 30 mph, there is no time left. That's what studiot meant. John
Most of the respondents figured this one out. It's not difficult, but it does seem to fly in the face of intuitive reasoning, which falters when you try to take the average of things that are already averages. Mark
I bet you some people still don't get it when you explain it to them because it seems counter intuitive. Dave
How very true, and how often that mistake is made - not for car speeds, but in business. I can't count the number of times I have dealt with managers (many with MBA's) who didn't understand the problem. My usual advice was, get rid of the ratios, go back to the original data, add it together and recalculate. When I would try to describe the statistical problems of dealing with ratios, they would typically dismiss it as some arcane detail. That is, until they met a real-life problem caused by misuse of ratios (averages), like budgets. John
Ok, I see, so it would require at least 90 MPH for 2 minutes to go down the hill, but at 90 MPH you would only have 40 seconds to do that. Sorry I am so slow to do that. I have never seen this before, so anyway that's pretty cool. I really want to share this with my math class.
I think you have it, but I'm not sure you're explaining it very well, so let me take a stab at it. To average 90 mph for the entire 2 mile trip, you would have to cover that distance in 80 seconds. The uphill mile has already taken you 2 minutes, or 120 seconds, making it impossible for you to travel both miles in less time than you've already used.