Problem Solving

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

okigbo 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

Time taken for the ride down = 300/(x+10)
Time taken for the ride up = 300/(x-8)

Now 300/(x+10) +135 = 300/(x-8)
20/(x+10) +9 = 20/(x-8)

x=10 clearly satisfies this

speed for the downhill journey = x+10 = 20 m/sec

It may take some time to solve the algebra from the post above - though it is absolutely correct and will always lead to the right answer. However, there is only 5 possible answers so try plugging the first:

300/(10+10) = 15

300/(10-8) = 150

150-15 = 135

Luckily this matches on the first try with A

Say we would have started with C (mid-pt of all answers)

300/(20+10) = 10

300/(20-8) = 25

25-10 = 15 so we know that 20 is MUCH too high so must be either A or B

I would then pick A - which is right but even if wrong I would know that B is right from elimination


Hope this helps

m&m wrote:
Luckily this matches on the first try with A

u matched the try with C

it asks for the speed for downhill journey which is x+10 and not x

Ur absolutely right t. Knowing x=10

avg speed is 10+10 = 20 C is correct

Thanks for correcting