For you motorists out there, here’s a brain teaser that has a moral to the story. Two motorists, Smith and Jones, are on family vacations. They are driving from point to point, a total distance of 810 miles. It’s all freeway with a speed limit of 75 mph and little or no traffic. Assumptions: (1) Both Smith and Jones will drive the entire trip in one day. (2) Each driver will make four rest stops along the way for all the usual needs when traveling with a family. (3) Each car is able to accelerate to highway speed instantaneously (unrealistic, of course, but simplifies the problem); likewise, each car is able to decelerate to a stop instantaneously (again, simplifies the problem). (4) Except for the rest stops, each car will maintain a perfectly constant speed the entire trip. Now, Smith obeys all speed limits without fail. He will drive 75 mph except when stopped. Also, he makes his rest stops relatively short (he has his wife and kids well trained!). Each of his stops will be 30 minutes long. Jones, on the other hand, is like most Americans; he drives over the speed limit. He will drive 80 mph the entire way (and no cops will notice). His stops are more typical in length—45 minutes each. Both drivers leave their point of origin at the same time. Here’s the $64,000 question, in two parts: (a) Which driver will arrive at his destination first, and (b) how much later will the second driver arrive at his destination? No calculators or pens/pencils for this one. Don’t even try to do it in your head. Just take a wild guess based on your driving experience. Who gets there first, and by how much time?
Posted on: Mon, 29 Jul 2013 01:04:31 +0000