I think this problem was on my SAT exam. Like the “fly-fly” problem, it is easy, if you just think about it. A man drives one mile at 30 miles per hour (mph). How fast would he have to drive another mile, in order to average 60 mph for the whole two- mile stretch?
A. 60 mph
B. 90 mph
C. 120 mph
D. None of the Above
If you chose B, 90 mph, you would be wrong. I know; 90 plus 30 equals 120, which divided by 2 is 60. But it doesn’t work that way. Consider that 60 mph is a mile a minute. Therefore, for the man to average 60 mph for two miles, he would have to drive that distance in two minutes. But he drives the first mile at 30 mph, thus taking up two minutes. Consequently, in order to average 60 mph for the whole two miles, he would have to drive the second mile in no time at all, which is impossible. Therefore, the correct answer is D, “None of the Above”.
Now, suppose we make the problem a little bit harder by asking how fast the man would have to drive the second mile to average 45 mph for the two-mile stretch? Ironically, the reason this problem is harder is because it has a viable solution.
We already know that the man used up two minutes driving the first mile at 30 mph. First, let’s figure out how much time it would take to average 45 mph for the whole two miles. Note that 45 miles per hour divided by 60 minutes per hour is 45/60 or 3/4 of a mile per minute. Now, 2 miles divided by 3/4 of a mile per minute is the same as 2 miles times 4/3 of a mile per minute, which equals 8/3 of a minute, or 2 and 2/3 minutes. [ 2÷3/4 = 2×4/3 = 8/3 ]
