##### Apr 04, 2006

**RAY:**At auction, my brother buys two slightly used Boeing 746's, with the idea of flying one of them around the world. Now, if you buy two of these planes, the auction house throws in a tiny island right on the equator.

Now, everyone knows that the circumference of the earth is 25,000 miles. But, sadly, neither of these planes, which have exactly the same range, can go 25,000 miles on a full tank of fuel.

Tommy does the math, however, and he figures out that if he flies one plane, and I fly the other plane as a refueling plane, I can give him some fuel and I can fly back to the little island

**TOM:**So, at some point, you're going to give me some fuel, you're going to turn back, and I'm going to continue on.

**RAY:**Exactly. We're both going to just make it. I'm going to give you some of my fuel, and with my remaining fuel, I just make it back to the island. And with your initial supply of fuel, plus what I give you from my plane, you continue on your journey, and sometime the next day, if we're lucky, you make it back to the same island.

**TOM:**Having gone all around the world.

**RAY:**Right. So the question is: What's the range of one of these 746's?

There are a few conditions that have to be met. For example, there's no wind, because that would add something complicated to the procedure. And, there's zero time to transfer the fuel and zero time to turn around. And one other thing: The earth isn't rotating for the 24 hours or so it takes to complete this whole thing.

Answer:

**RAY:**It's a simple algebra problem.

Let's call 'x' the range of a 746 plane.

Let's look at my plane first, the refueling plane. The best I can do for you is to give you a third of my fuel. I'll use a third of the fuel flying right alongside you, and I'll use a third getting back to the island.

I can't give you more than a third of the fuel. Why? Because I wouldn't make it back if I gave you more, and having used only a third of your fuel, you'd have no room for any more than a third of a tank of fuel.

**TOM:**Exactly. I like it!

**RAY:**Now, let's call the distance I fly alongside you, Y. The distance I fly back is also Y, and the third of a tank of fuel that I give you lets you fly an additional distance, Y, that gets you to the island. So clearly 3Y equals X. You still with me?

**TOM:**I'm with you. Keep going!

**RAY:**So, now we know that X plus Y equals 25,000 miles, right?

And 3Y equals X, so 4Y must equal 25,000 miles. Y then equals 6,250 miles, which is how far I fly alongside you.

X, then, equals 18,750 miles.

Of course, you don't make the island. You miss by a mile. Why? Because I didn't give you all the fuel.

**TOM:**Thanks. I appreciate that.

**RAY:**Do we have a winner? The winner is Dick Ottman from Bear Lake, Minnesota. And for having his answer selected at random from among all the correct answers that we got, Dick is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com where he can get his Mothers's Day shopping out of the way early.

Would buy your mother something from Car Talk?

**TOM:**Me? No, because you already gave her one of everything. I'm stuck buying flowers.