Annika hikes at a constant rate of 12 minutes per kilometer. She.....

Lemme try explaining how I solved the question.

A can hike 1 kms in 12 minutes. So in 45 minutes she can hike 3.75 kms.

No she has hiked 2.75 kms when she realized that she has to return to the starting point.

Basically, she has to cover 3.75 kms in 45 mins. Since she has already hiked 2.75 Kms and this distance has to be covered on her way back in those 45 minutes, she is left with only 3.75-2.75= 1 km. And in this 1 km, she has to travel towards east and then return i.e. she will cover .5 kms to the east and .5kms return distance.

So she traveled total of 2.75+.5= 3.25 kms towards east

C is the answer
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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 = 3.25

Answer: C

Cheers,
Brent

Sorry, I don't understand how you get 3.75.
Annika has hiked 2.75 km during 33 minutes (if her constant speed is 1km every 12 min). So when she realizes she has to go back, she has 45-33= 12 minutes left. It leaves her the time to advance for another 6 minutes (0,5 km). The time to go back would be 39 minutes for all the distance (2.75+0,5 = 3.25 km). My answer was C (but apparently wrong). Could you please explain what I am doing wrong? thanks

I'm with you YulSob on this one, I've tried various approaches and continue to come up with C as the answer...where's Bunuel when we need him?

Actually the correct answer is C) 3.25 km. This problem is from the manhattan word strategy guides and apparently there is a type that i wanted to confirm. Sorry for the trouble caused.
My solution is as under;
Set up two R x T =D cases.
1. 1/12 km/ min x T = 2.75

from which T= 33 mins.

We know total journey time now is 45 +33 =78.
The rate is the same ie 1/12km/min.

set up second R x T =D case.

1/12 km/min x 78 = 6.5 km
Now the total journey would be halved as distance would be same in each direction. 6.5/2 =3.25.
C.

A slightly different way of solving with just one equation.
Assume the distance to be travelled further east =x

Now in another 45 min, Annika would travel 2x + 2.75 km at a speed of 1/12 km/min.

Putting in a RTD equation
2x+2.75=45/12
x=0.5
x+2.75=3.25

Answer C

Hello Everyone,


You do not need to know that she already hiked during 33 minutes to find out the solution.

We know that she already hiked 2.75km.

She hikes one kilometer in 12 minutes, so she hikes at 5 km/h. She has 45 minutes left. So she can walk 5*(45/60) = 3.75 more kilometers.

She would have walked 2.75 + 3.75 = 6.50 km. Since the way up is as long as the way down, she hiked 6.5/2 = 3.25km

Answer C.

A's rate is 5kph
in 3/4 hour she hikes 3.75k
let d=distance from 2.75 miles east of start to turnaround point
2d+2.75=3.75k
d=.5k
.5k+2.75k=3.25k total distance hiking east
C.

can Experts please share a event detailed solution I am so lost here.

Since Annika has already hiked 2.75 km if she were to turn around at that moment it would take her 33 minutes to return home. She has 45 minutes to return home. 45-33=12. She needs half of that time to return. So if you split the remaining 12 minutes in half (one half travel east, one half return home) she has 6 additional minutes to walk east which is .5 km. So 2.75+.5=3.25 km.

Here's my explaination

Annika covered

1km in 12 mins
2km in 24 mins
3km in 36 mins
4km in 48 mins

She travelled 83.3mts/min (1000mts/12mins)

83.3*3 = 249.9mts

In 45 mins she travelled 4 - 2.49 = 3.75.

Answer D

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The answer is C
Total distance traveled in 45 min = 45*1/12=15/4=3.75
Now this 3.75 contains 2.75 and the distance x that she traveled when she realized that she had to go back in 45 min.
Now this x distance is covered twice in 45 min minutes once due east and once while returning .
So 2x+2.75=3.75
2x=1 therefore x=0.5
Now total distance hiked due east =2.75+0.5=3.25

The way I approached this problem was by finding the total time that Annika hiked first.
Rate given = 12km/min

The question says that she had already traveled 2.75 km east. In this time, she traveled 2.75 km * (12min/1km)= 33 minutes.

Next, we are told that she has 45 minutes to return back to the start of the trail. So we should add the 33 minutes that she had already hiked to the 45 minutes she has to make it back to the start of the trail. 33+ 45 = 78.

In total, she will be moving for 78 minutes.

Take the total time and multiply it by her rate. (Careful here because the rate was provided in minutes/km. You have to either invert the given rate or calculated total time).

78 min *( 1km/12min) = 13/2 miles = 6.5 miles.

Total travel distance 6.5 miles. We are told she traveled 2.75 miles and then continued east before turning around. If you divide 6.5 km in half, you will get 3.25. this is the halfway mark for the total trip.

If her rate is 12 minutes per kilometer, then in 60 minutes, or in 1 hour, she walks 5 kilometers, and thus her rate is 5 km/hr.

Since 45 minutes = 3/4 hour, in 45 minutes Anika travels 5 x 3/4 = 15/4 = 3.75 km.

She has already walked 2.75 km, and she will walk an additional 3.75 km in the next 45 minutes. So, in total, she will have traveled 2.75 + 3.75 = 6.5 km for her entire hike.

Thus, she has to turn around when she is at the halfway point, when she has traveled 6.5/2 = 3.25 km east.

Answer: C
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Algebra? Don't mind if I don't! Let's PITA (Plug In The Answers) instead. She has already hiked 2.75 miles east, so A and B are out. We are left with C, D, and E.

Let's try D.
She hiked a total of 3.75 miles east. That means she has 1 more to go before she turns around plus 3.75 miles west to get back where she started. That's 4.75 miles, which takes her 4.75*12...oh wait, that's more than 45 minutes. D is out. We need something smaller (and we already eliminated A and B), so it must be C.

Answer choice C.


ThatDudeKnowsPITA

Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers 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 kilometers total did she hike east?

A) 2.25
B) 2.75
C) 3.25
D) 3.75
E) 4.25

The easy way to understand this question.
She hikes 12 min per km i.e. 1 km in 12 min > 5 km in 60 min. So her speed is 5 km/hr

now make a simple diagram to understand the question

---------2.75km----------+++++++ Here --- is total 2.75 km which she travelled and ++++ is the additional distance(in east) say x.

----------------------------+++++++ Now, to move to the starting point, she first travel x in the east, then turns back, again travel x and finally rest 2.75

So total distance = 2x + 2.75, time taken = 45 min

D X S = T, 2x + 2.75 = 5 x 45/60, So, x = 0.5 km

So distance in east = x + 2.75 = 3.25

Hope its clear