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SecondWind 08-19-2009 08:59 PM

If you enjoyed the SATs , you might want to try this brainteaser I thought of on a run today:

Penny ran once around the edge of a round lake that was one mile straight across. She was pleased with the length of her run because it was about the same distance as the race she's training for. How long is her upcoming race?

(A) 2 miles
(B) 5 kilometers
(C) 5 miles
(D) 10 kilometers

Good luck!

This was my brain on endorphins. OK, I'm weird--and I also used to write test questions. Post your answer--or beg me a little and I'll explain.

Complete Pete 08-20-2009 08:30 AM

She's running a 5k, no? Pi times D = 3.14?

SecondWind 08-20-2009 04:32 PM

Bravo. As you explained, the distance around the lake is diameter times pi, or 1 mile x 3.14(approx)= about 3.14 miles. Since 5 kilometers is just over 3.1 miles, (B) is the best answer.

Oh... and you're clamoring for a bonus question? Well, OK...

Arkady's town has an area of 6.25 square miles. His town boundaries are in the shape of a square. He runs once around the town to prepare for a race of a similar distance. Is Arkady training for:

(A) A 2.5-mile race
(B) A 10K race
(C) A 10-mile race
(D) A marathon

Consider this a warmup for the school year!

Complete Pete 08-21-2009 07:26 PM

That would be a 10 miler.

Are = s squared, where s = the length of one side.

The square root of 6.25 is 2.5, therefore 2.5 per side

P=4s

SecondWind 08-22-2009 02:11 AM

Chalk up another point for Complete Pete. Answer is indeed (C), a 10-mile race.

And now one for those who are verbally inclined:

What is the rationale behind the names of the two people in the previous problems?

Ella 08-22-2009 08:06 AM

Penny Arcade.

Wondered where the **** you got the name Arkady from!!

Wonder if Pete would do my Research test for me. He seems to like these tests alot!!

SecondWind 08-22-2009 12:50 PM

Yep, Ella, I named the characters after Penny Arcade. Since Arcade is not a person's name, Arkady is the best I could do. It's a Russian boy's name that I've heard from time to time.

OK, let's see who's up to having their brain teased on the weekend:

K.R. went for his Saturday run. Half of the distance of his run was on flat road, a third of the distance was uphill, and three miles was downhill. How far was K.R.'s run?

Ella 08-23-2009 05:31 AM

18 miles.

Complete Pete 08-23-2009 11:08 AM


half point for Ella.

You didn't show your work.

Ella 08-23-2009 11:13 AM

18/2=9 miles flat
18/3=6 miles up
9+6=15
15+3miles down=18miles

SecondWind 08-24-2009 11:33 AM

Righto, Ella. Pete, you are quite the taskmaster (even more so than I am). Anyone else have any brainteasers to post? I'd like to try one for a change...

Ella 08-24-2009 11:41 AM

But I got it right, so I still get full marks. You get the half mark if your working out is mostly correct but your answer is wrong!

Floridaboiler 08-25-2009 08:32 AM

Wow,
You guys are like smart and stuff!

SecondWind 08-26-2009 08:52 AM

OK, here's another one...

Three teams competed in a 1600-meter relay (four runners per team). The results were as follows:

All the first runners had exactly the same time.

On Team 1, the 2nd, 3rd, and 4th runners had the same time as well.

On Team 2, the second runner's time was 10% longer than the first runner, the third runner's time was 10% shorter than the second runner, and the fourth runner's time was two seconds longer than the third runner.

On Team 3, the second runner's time was 10% shorter than the first runner, the third runner's time was 10% longer than the second runner, and the fourth runner's time was two seconds longer than the third runner.

In what order did the teams come in, or did they tie?


Ella 08-26-2009 11:25 AM

Team 3
Team 1
Team 2

SecondWind 08-26-2009 01:35 PM

Right!

Of course, Complete Pete will require you to show your work. He's a stickler for Completeness.

Complete Pete 08-27-2009 09:35 AM

Pete ran 10 miles on Monday. On Tuesday he was a bit tired so he decreased that by 10%. When Wednesday rolled around he was feeling a bit better so when he ran he increased his previous day's run by 10%.

How far did Pete run on during those three days?

Complete Pete 08-27-2009 09:51 AM

Repete was running on the dreadmill.

He ran for 45 min @ 10:00 pace
Then he ran for 45 min @ 9:00 pace

What was his average pace?

Ella 08-27-2009 09:54 AM

Monday 10miles
Tuesday 10% of 10 =1, 10-1=9miles
Wednesday 10% of 9 = 0.9, 9+0.9=9.9miles

Pete ran a total of 28.9 miles.

Ella 08-27-2009 10:02 AM

9:30

QuixoticNotions 08-27-2009 08:31 PM

No, 9:28!

45 min at 10 = 4.5 miles
45 min at 9 = 5 miles
Total = 9.5 miles
45 min + 45 min = 90 min


90 minutes / 9.5 miles = 9.4737 minutes per mile
.4737 x 60 = 28.42

9:28/mile


These are all too easy!

Ella 08-27-2009 10:26 PM

I was lazy. I rounded up rather than calculate what 0.47 was in minutes.

So Pete would give me zero marks for that one, cos I didn't show my working out!

SecondWind 08-27-2009 11:55 PM

I agree with Ella on the 28.9 mile total run (Complete Pete's problem, post #17).

I agree with QuixoticNotions' 9:28 (approx.) pace in answer to Complete Pete's second problem, post #18. And she showed her work well.

Nicely devised problems, both.

I'd like to see a problem from QuixoticNotions--one that isn't "too easy."

QuixoticNotions 08-28-2009 09:47 AM

but that's what I'm having to do with my homework already! (In school to be a teacher. Right now is math class)

How about I give you guys a bunch of data points and you come up with problems using those data points. No reason

Complete Pete 08-28-2009 10:18 AM

Sounds good.

I was expecting you to ask the maximum velocity of an unladen swallow.


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