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Hiking

by Priyaranjan » Sun Dec 06, 2015 2:24 am
Q. Annika hikes at a constant rate of 12 minutes per kilometre. She has hiked 2.75 kilometres east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometres total did she hike east?

A) 2.25
B) 2.75
C) 3.25
D) 3.75
E) 4.25
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by GMATGuruNY » Sun Dec 06, 2015 3:35 am
Priyaranjan wrote:Q. Annika hikes at a constant rate of 12 minutes per kilometre. She has hiked 2.75 kilometres east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometres total did she hike east?

A) 2.25
B) 2.75
C) 3.25
D) 3.75
E) 4.25
Since Annika hikes at a rate of 1 kilometer per 12 minutes, the distance traveled in the final 45 minutes = rt = (1 kilometer/12 minutes)(45 minutes) = 45/12 = 15/4 = 3.75 kilometers.

Total distance traveled = (initial distance hiked) + (distance hiked in the final 45 minutes) = 2.75 + 3.75 = 6.5 kilometers.

Since half of this distance is hiked east, the total distance hiked east = 6.5/2 = 3.25 kilometers.

The correct answer is C.
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by Brent@GMATPrepNow » Sun Dec 06, 2015 8:07 am
Priyaranjan wrote:Q. Annika hikes at a constant rate of 12 minutes per kilometre. She has hiked 2.75 kilometres east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometres total did she hike east?

A) 2.25
B) 2.75
C) 3.25
D) 3.75
E) 4.25
Annika's speed 12 minutes per kilometer
In other words, she walks at a speed of 1/12 kilometer per minute.

She has already waked 2.75 km

Let x = the additional # number of km she walks EAST before turning around.
This means the number of kilometers she will hike from this point = x + x + 2.75 kilometers

She must walk this distance in 45 minutes at a rate of 1/12 kilometer per minute

Distance = (rate)(time)
So, x + x + 2.75 = (1/12)(45)
2.75 + 2x = 3.75
2x = 1
x = 0.5

So, the TOTAL distance Annika walks EAST = 2.75 + 0.5 = [spoiler]3.25 = C[/spoiler]

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by jain2016 » Sat Jan 30, 2016 9:46 am
Let x = the additional # number of km she walks EAST before turning around.
This means the number of kilometers she will hike from this point = x + x + 2.75 kilometers
Hi Brent ,

Can you please advise that why did you do x+x+2.75, why not x+2.75?

Please advise.

Many thanks in advance.

SJ
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by Brent@GMATPrepNow » Sat Jan 30, 2016 11:04 am
jain2016 wrote:
Let x = the additional # number of km she walks EAST before turning around.
This means the number of kilometers she will hike from this point = x + x + 2.75 kilometers
Hi Brent ,

Can you please advise that why did you do x+x+2.75, why not x+2.75?

Please advise.

Many thanks in advance.

SJ
Let's call the point where she's standing (2.75 km from her starting point) point Q.
From here, if she walks an additional x km EAST before turning around, then she walks x km.
Then she must turn around and walk x km WEST to get back to point Q.
So, when she reaches point Q, she has walked a total of x + x km
She still needs to travel from point Q to the start of the trail, so she must walk a TOTAL of x + x + 2.75km

Does that help?

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by ceilidh.erickson » Sat Jan 30, 2016 3:35 pm
I think it helps to draw a picture of this one. Let the black represent her initial 2.75km, then the red is the unknown distance that she runs further east, plus the total distance that she runs back west:

Image

Here, it's easy to see that the total distance she will go in that remaining 45 minutes is x + x + 2.75.
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by ceilidh.erickson » Sat Jan 30, 2016 3:38 pm
Also, I want to point out that this question is almost a direct plagiary of PS #98 in OG2016. Please don't study from sources that plagiarize the official guide! You want to study from sources that create content that is original, but GMAT-like.

What is the source of this question?
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by Matt@VeritasPrep » Sun Jan 31, 2016 7:24 pm
ceilidh.erickson wrote:a direct plagiary
... and there's my vocab word of the day! Nice choice, cannot believe I'd never heard of that word before.
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