Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start...

AAPL wrote: ↑

Wed Jan 13, 2021 4:38 pm

Manhattan Prep

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

OA C

Solution:

If her rate is 12 minutes per kilometer, then in 60 minutes, or 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.

Alternate Solution:

Suppose Annika walks x km east before turning back. In total, she will have walked 2x + 2.75 km in 45 minutes. Since she walks one kilometer in 12 minutes, 2x + 2.75 km takes her (2x + 2.75)*12 = 24x + 33 minutes to walk. Thus, we have:

24x + 33 = 45

24x = 12

x = 1/2 = 0.5

Therefore, Annika walked 2.75 + 0.5 = 3.25 km east.

Answer: C

AAPL wrote: ↑

Wed Jan 13, 2021 4:38 pm

Manhattan Prep

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

OA C

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