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jclalor

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A race car averages 30 MPH around an oval race track on the first lap. How fast must he go on the second lap to average 60 MPH for the 2 laps?



I'm going to say 30 ..but I first thought 90 as well.
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It is impossible to average 60 MPH for both laps.



I agree. If you did a 1 mile oval track, 30 MPH would take 2 minutes. To average 60MPH, you wuld need to average 1 lap a minute, and you already wasted the 2 mintues on the first lap, therefore impossible to get the avg up to 60.
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I agree. If you did a 1 mile oval track, 30 MPH would take 2 minutes. To average 60MPH, you wuld need to average 1 lap a minute, and you already wasted the 2 mintues on the first lap, therefore impossible to get the avg up to 60.



I dig your point, but I don't think that's what the riddle is asking, at least how I'm reading it. You are right in that you wouldn't ever complete the two laps in two minutes, but the question isn't asking that. It wants to know what speed you'd have to go to have an average speed of 60 mph. So as I was mentioning above, assuming you could instantly speed up to 90mph at the start of the second lap, you'd have an average speed for the two laps of 60mph. Right?

Average of two numbers = (first number + second number)/2.

Ergo: 60 = (30+x)/2

2x60 = (30+x)/2 x2 (multiply both sides by two)
120 = 30 + x

then
120 -30 = 30 + x -30 (subtract 30 from both sides)

so

x = 90

You're right that it'd take 45 seconds to do the second lap, which added to the two minutes you took to do the first lap would be 2:45. Yes, you could never do the second lap fast enough to average one minute per lap once you've taken two minutes to do the first lap (unless you could instantly teleport yourself or something cool like that) but that's not what the question is asking. With a second lap of 90mph the AVERAGE of the two lap speeds WOULD be 60.

Comes down to the whole add/subtract before you multiply/divide thingy. Or is it the other way around?:P

At least that's my take on it.

Elvisio "always called to do the problem at the board immediatly after fantasizing about the hot chick in class" Rodriguez

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The length of the track does not matter.

The driver averaged 2 minute miles for X miles. After another X miles, the driver needs to have averaged 1 minute miles for 2X miles. Therefore, he needs to do 0 minute miles for the second lap.

So freakflyer9999 is right.
"Great spirits have always encountered violent opposition from mediocre minds." -Albert Einstein

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Those that said 90mph, check your math:

Assuming the track is 30mi. long (for easy math) your driver has covered 60 miles, the first half in an hour, and the second half in 20 minutes. That's 60 miles in 80 minutes, or 45mph.
"Great spirits have always encountered violent opposition from mediocre minds." -Albert Einstein

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