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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Skier Lindsey Vonn completes a straight 300-meter downhill run in t se
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06 May 2021, 00:14
06 May 2021, 00:14
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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
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Skier Lindsey Vonn completes a straight 300-meter downhill run in t se
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06 May 2021, 05:08
06 May 2021, 05:08
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GeminiHeat 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
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
The ride up the mountain took 135 seconds longer than her run down the mountain
Start with a word equation: (time going UP mountain) = (time going DOWN mountain) + 135
time = distance/speed
We can now write: 300/(x - 8) = 300/(x + 10) + 135
Multiply both sides by (x - 8) to get: 300 = 300(x - 8)/(x + 10) + 135(x - 8)
Multiply both sides by (x + 10) to get: 300(x + 10) = 300(x - 8) + 135(x - 8)(x + 10)
Divide both sides by 5 to get: 60(x + 10) = 60(x - 8) + 27(x - 8)(x + 10)
Divide both sides by 3 to get: 20(x + 10) = 20(x - 8) + 9(x - 8)(x + 10)
Expand both sides to get: 20x + 200 = 20x - 160 + 9x² + 18x - 720
Rearrange and simplify to get: 9x² + 18x - 1080 = 0
Divide both sides by 9 to get: x² + 2x - 120 = 0
Factor to get: (x + 12)(x - 10) = 0
So, EITHER x = -12 OR x = 10
Since x can't be the speed, we know that x = 10
What was her average speed, in meters per second, during her downhill run?
Her downhill speed = x + 10
Since x = 10, her downhill speed = 10 + 10 = 20
Answer: C
Cheers,
Brent
gmatclubot
Re: Skier Lindsey Vonn completes a straight 300-meter downhill run in t se [#permalink]
06 May 2021, 05:08
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