NJR: Maths Challenge

[Mulboyne]

I just came across this poser and answer so I thought I'd throw it out there in case any FG brains care to try to come up with the solution.

You are asked to drive a car two laps of a circuit at an overall average speed of 80 mile per hour. At the exact moment you complete the first lap, you discover that you have so far averaged 40 mph. How fast will you need to go over the second lap to to get your overall average speed up to 80 mph?

Even if this thread is thoroughly ignored, I'll post the answer later.

[Yokohammer]

Um ... the speed of light?

To make things simple, let's assume that each lap is a distance of 80 miles (big laps). That means you need to cover the 160 miles (two laps) in two hours to make an average speed of 80 mph. So, if your speed was only 40 mph after the first lap, you have already spent two hours completing the lap. Your time is up ... unless you complete the second lap in *no time*.

OK, now my head hurts ...

[sublight]

Impossible. To get a total average of 80mph, you would need to do the second lap in no time at all. i.e., at infinite speed.

[Iraira]

I'm getting minuses for the time for lap 2, so I'm going to go have dinner.

[CrankyBastard]

I'll post the answer later.

Good, that'll save me the bother of trying.

[Kuang_Grade]

Initially, I fell into the trap of thinking that 1 lap equals 50% of the distance covered way of thinking that would work ((lap1speed*.5)+(lap2speed*.5)) but using my old LSAT/GMAT test training, I thought that if it was that easy, then Mulboyne wouldn't have posted it.

I thought about it some more and the stray thought of 'this sounds like some sort of problem using special averages from that hated Statistics class you barely got a C in more than a decade ago'...so I poked around a bit and this problem requires a special average formula called a harmonic mean, which you use to average certain kinds of ratios (which is what MPH is) and the formula to use when only using 2 numbers would be

(2*lap1speed*lap2speed)/(lap1speed+lap2speed)

in this case, with X being the number we are seeking
or (2*40*X)/(40+X).

But the answer is unsolvable because of the the bigger X gets, it can't overcome the 80mph threshold....the bigger the number you put in for X, the closer the average gets to 80mph but it will never cross it. In this formula, X can never exceed lap1speed by more than 199.9999999999infinity%

[Tsuru]

Yokohammer has the right answer... no matter how big the circuit is, you have used all your time by the time you completed the first round, hence your average speed for the second lap needs to be infinity miles per hour.

[Mulboyne]

[omae mona]

I'm trying to figure out if I can use this logic to stop the cop from issuing me a ticket next time I am pulled over for speeding.