BTGmoderatorDC wrote: ↑

Fri Aug 20, 2021 10:39 pm

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

Source: Manhattan Prep

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