Some help with sat math problem

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1

<p>Jake rides a lift to the top of a maountain at a speed of 5 miles per hour. He then skis straight back down the slope to the bottom of the ski lift at an average speed five times faster than he went up the mountain. If the whole trip took 30 minutes, how long is the ski slope?</p>

<p>a. 1 mile
b. 15/7 miles
c. 17/6 miles
d. 25/6 miles
e. 5 miles</p>

<p>my attempt at a solution:</p>

<p>d=5t
d = 25T/5</p>

<p>From here on I tried plugging in the answers for the distance but they all seem to work. Then I found another way</p>

<p>at 5mph he's traveling at 1/12 miles per minute and at 25mph on the way down its 5/12 mpm. The I multiplied 1/12 by 5 to get 25/12 and did the same for 5/12 and got 25/12. I added up the distance and got 25/6 but im not sure at all if its correct.</p>

<p>Im pretty confused with this one so any algebraic solution would really help. Thanks.</p>

2

<p>Is the answer “D”? If so, plug in the answer choices. </p>

<p>Here’s why answer D works:
You know the distance is the same to go up the slope and down the slope, so divide 25/6 by 2. You get 25/12.</p>

<p>Now set up a proportion for the upslope portion: 5mi/60 min=(25/12mi)/x min; x= 25.
AND 25mi/60 min=(25/12)mi/ x min; x= 5 </p>

<p>Then, add the total minutes, and the answer is 30.</p>

<p>Hope that helped!</p>

3

<p>OK, here we go again! This is ALL you need to know:</p>

<p>5 x 25 / (5 + 25)
Simplify to get 25/6.</p>

<p>Took all of 8 seconds!</p>

<p>The reason there is only S1.S2/S1+S2 is that the round trip was 1/2 hour. No need to multiply by 2 and then divide by 2 because of 1/2 the time.</p>

<p>================
Now, let all the people show up with extended and derived versions of d=rt and try to convince it is just as fast to fiddle with numbers for a few minutes.</p>

4

<p>xiggi, could you elaborate on your method? ive heard of it, but im not sure quite how it works, mind explaining?</p>