Mrs. Riddledude and I decided to take a trip one day. So we get in the car and Mrs. RiddleDude drives the first 40 miles and I drive the rest of the way. We arrive at our destination and we get out of the car, glance at the foliage, and Mrs. RiddleDude says, “okay, let’s get a cappuccino and get out of here.” So we turn around and head home on the same road that we used to get there, okay? Mrs. RiddleDude drives the first leg of the trip, and I drive the last 50 miles home.
Anyway, when I get home the neighbor says, “How was the trip?” And I say, “I was with my wife, how good could it have been?” And he says, “Well, who did the driving?” And I explain exactly what I just said. “On the way there Mrs. RiddleDude drove the first 40 miles and I drove the rest. On the way back Mrs. RiddleDude drove the first leg of the trip and I drove the last 50 miles.”
He said, “Yeah, but who did most of the driving?” I said, “Well, you can figure it out, in fact you can even figure out how much more of the driving was done by that person.” Now, I didn’t say how long we were gone, how far we went, whose car we took, who bought the gas or any of those things. So the question was who drove the most miles and how many more did that person drive?
July 24th, 2010 | Category: 
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40 + x = y + 50
-> x = y + 10
driven distance:
Mr. Riddledude: x + 50 = y + 60
Mrs. Riddledude: 40 + y
where y is a positive number
So Mr. Riddledude drove 20 more miles.
Mrs riddledude=40 miles
Mr riddledude =50 miles
The initial point(x) from where they started their journey isn’t specified . It may be 10 miles nearer to where ever they wanted to go than their home. Mrs. R drove the initial part starting from x and Mr. R drove while on the way back.
Det, you nailed it.
The answer is I drove 20 more miles than she did.
You could make it complicated, you could say “Well, gee, I don’t have enough information. I don’t know the distance, I don’t know the speed, I don’t know anything, wawww, wawww,” but I always like to boil these problems down to what I call the limiting case.
I said that the Mrs.drove the first 40 miles and I drove the rest, okay. And then on the way back she drove the first leg and I drove the last 50.
You could make the distance anything you want, but let’s make it 60 miles. So she drove the first 40 which means I drove the last twenty. On the way home, since I drove the last 50 miles, that means she drove the first ten. In that instance I drove a total of 70 miles and she drove a total of 50 miles. I drove twenty more miles than she did.
If it were 200 miles, then on the way there she drove the first 40 and I drove 160. On the way home, I drove the last 50 so she drove 150. She totaled 190 and I totaled 210. I will always be 20 miles more regardless of the total miles.
Great job, Great riddle! You’re today’s winner.