MBAhereIcome wrote:
Skier Lindsey Vonn completes a straight 300-meter downhill run in t seconds and at an average speed of (x + 10) meters per second. She then rides a chairlift back up the mountain the same distance at an average speed of (x - 8) meters per second. If the ride up the mountain took 135 seconds longer than her run down the mountain, what was her average speed, in meters per second, during her downhill run?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
We can skip the algebra altogether and Plug In The Answers (PITA).
x has to be greater than 8 or she will be going backward on the chairlift. x+10 is therefore greater than 18. A and B are out.
Let's plug in D.
She skis down at 25mps. 300 meters will take 12 seconds.
She skis down at x+10, so x=15.
She rides up at x-8, so 7mps. 300 meters will take somewhere around 40-45 seconds.
That's a difference of way too little time. D is out.
It might not be obvious whether we need something smaller or something larger, but we only have C and E remaining, so we can try either. Let's do C.
She skis down at 20mps. 300 meters will take 15 seconds.
She skis down at x+10, so x=10.
She rides up at x-8, so 2mps. 300 meters will take 150 seconds.
That's a difference of 135 seconds. Yay!
Answer choice C.
ThatDudeKnowsPITA