## Sunday, August 21, 2011

### Manhattan GRE's Math Beast Challenge problem for this week

This Week's Problem: "Clement Walks"

Q: Clement walks around an oval-shaped track at a constant rate of 50 seconds per lap. If 18 laps equal a mile, how many miles does Clement walk in 54 minutes?

A:

(A) 2
(B) 2.5
(C) 3
(D) 3.6

This took me about a minute to figure out. It's just quick algebra. The more gifted among you can doubtless do this in your heads. (The answer will be posted later in the comments.)

_

Horace Jeffery Hodges said...

I think 18 laps is 15 minutes, so one mile takes 15 minutes. In 54 minutes, one would walk more than three miles, so I think "D" is the answer.

And it took me too long to do that in my head . . . a couple of laps worth, I guess.

Jeffery Hodges

* * *

Kevin Kim said...

Bingo. There are several different approaches one can use, but it sounds as if you used this approach:

1 lap is done in 5/6 minutes.

Therefore:

18 laps are done in 15 minutes. (This can be seen by setting up a proportion.)

1 mile in 15 minutes = 4mph.

4 mph for .9 hours (54 minutes) = 3.6 miles.

QED. (Quirky, erotic, delicious.)

Horace Jeffery Hodges said...

Actually, I just thought, "Hmmm . . . at fifty seconds per lap, six laps takes five minutes, so eighteen laps is fifteen minutes."

And I took it from there.

Jeffery Hodges

* * *

Kevin Kim said...

That's probably an easier way to do it.

Surprises Aplenty said...

Since I only had to be close enough to exclude the other answers, I simply looked at 54/18. If it took a minute to do a lap, '3 miles' would be the answer. As the laps were slightly faster, it must be '3.6 miles' or D. I didn't see the need to fine-tune my calculation. Lazy, I guess.

Kevin Kim said...

Even faster!

This problem is so much easier than that damn "spinach rows" problem.