Skier Lindsey Vonn completes a straight 300-meter downhill r

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Skier Lindsey Vonn completes a straight 300-meter downhill r

by BTGmoderatorDC » Sun Dec 30, 2018 10:03 pm

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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

OA C

Source: Manhattan Prep

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Source: Beat The GMAT — Problem Solving | Sun Dec 30, 2018 10:03 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Dec 31, 2018 5:10 am

BTGmoderatorDC 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

Downhill speed - uphill speed = (x+10) - (x-8) = 18.
Implication:
The downhill speed is 18 mps greater than the uphill speed.

We can PLUG IN THE ANSWERS, which represent the downhill speed.
Since the downhill speed is 18 mps greater than the uphill speed, the correct answer must be GREATER THAN 18.
Eliminate A and B.

The remaining answer choices imply the following:
C: downhill speed = 20, uphill speed = 20-18 = 2
D: downhill speed = 25, uphill speed = 25-18 = 7
E: downhill speed = 30, uphill speed = 30-18 = 12
Since the value in red does not divide evenly into the 300-meter distance, D is almost certain to be incorrect.
When the correct answer is plugged in, uphill time - downhill time = 135 seconds.

C: downhill speed = 20, uphill speed = 20-18 = 2
Time to travel 300 meters uphill at a speed of 2 mps = 300/2 = 150 seconds.
Time to travel 300 meters downhill at a speed of 20 mps = 300/20 = 15 seconds.
Uphill time - downhill time = 150-15 = 135 seconds.
Success!

The correct answer is C.

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Thu Jan 03, 2019 9:17 am

Backsolving is the preferred approach for this one

300/(x-8) - 300/(x+10) = 135

We are asked for the value of x+10

So we can start with C = X+10 = 20
So x = 10
300/2 - 300 / 20 = 135

It Satisfies. Hence answer is C.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Feb 07, 2019 6:25 pm

BTGmoderatorDC 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

OA C

Source: Manhattan Prep

We can let the time going down = 300/(x +10) and the time going up as 300/(x - 8), thus:

300/(x +10) + 135 = 300/(x - 8)

Multiplying by (x + 10)(x - 8), we have:

300(x - 8) + 135(x + 10)(x - 8) = 300(x + 10)

20(x - 8) + 9(x + 10)(x - 8) = 20(x + 10)

20x - 160 + 9(x^2 + 2x - 80) = 20x + 200

20x - 160 + 9x^2 + 18x - 720 = 20x + 200

9x^2 + 18x - 1,080 = 0

x^2 + 2x -120 = 0

(x + 12)(x - 10) = 0

x = -12 or x = 10

Since x can't be negative, x must be 10. Therefore, the speed for the downhill run was 20 meters per second.

Answer: C

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