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Here's an interesting question of the type typical of IQ tests. The thing to remember about such tests is to winnow away almost everything from the questions and leave only what is actually being asked.

That said, here is one that stumped even Einstein at first glance, and it fooled his friend.

Try the question before reading the except from Einstein's letter at the bottom.

Q1- Distance, Time, and Speed An old car has to travel a 2-mile route, uphill and down. Because it is so old, the car can climb the first mile—the ascent—no faster than an average speed of 15 mi/h. How fast does the car have to travel the second mile—on the descent it can go faster, of course—to achieve an average speed of 30 mi/h for the trip?

Problem 1 was sent to Albert Einstein by his friend Wertheimer. Einstein (and his friend Bucky) enjoyed the problems and wrote back to Wertheimer. Here is part of his reply:

Your letter gave us a lot of amusement. The first intelligence test fooled both of us (Bucky and me). Only on work-ing it out did I notice that no time is available for the down-hill run! Mr. Bucky was also taken in by the second example, but I was not.

Such drolleries show us how stupid we are!

(See Mathematical Intelligencer,Spring 1990, page 41.)

Q1- Distance, Time, and Speed An old car has to travel a 2-mile route, uphill and down. Because it is so old, the car can climb the first mile—the ascent—no faster than an average speed of 15 mi/h. How fast does the car have to travel the second mile—on the descent it can go faster, of course—to achieve an average speed of 30 mi/h for the trip?

what am i missing here?
why is the answer not 45 mi/h?
there is no time factor mentioned in the problem.
???

Q1- Distance, Time, and Speed An old car has to travel a 2-mile route, uphill and down. Because it is so old, the car can climb the first mile—the ascent—no faster than an average speed of 15 mi/h. How fast does the car have to travel the second mile—on the descent it can go faster, of course—to achieve an average speed of 30 mi/h for the trip?

I'm only in the 140s (U.S> scale), but it didn't take me long to figure this one out.

The problem is lends itself to easy calculation because it uses numbers that divide easily into 60.

The whole trip is two miles (one mile up and down). At 30 mph, we know that is one mile every two minutes. That means the trip has to be completed in 4 minutes. But at 15 mph, the car takes 4 minutes to make the climb, meaning the return trip has to be instantaneous to make the 30 mph mark.

PLEASE tell me that the correct answer is “30mph”!