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
Skier Lindsey Vonn completes a straight 300-meter downhill r
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Downhill speed - uphill speed = (x+10) - (x-8) = 18.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
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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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.
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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We can let the time going down = 300/(x +10) and the time going up as 300/(x - 8), thus: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
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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