Question

Kara and Lindsey both hike in separate directions from their campsite, with Kara hiking straight to the east and Lindsey hiking straight north. At
2:00 p.m., Kara hiked twice as far to the east as Lindsey hiked to the north. At 2:30 p.m., Kara had covered another mile, while Lindsey had
covered another half of a mile. If x represents Lindsey's distance, in miles, from the campsite at 2:00p.m., what function could be used to
represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m.?

Answer 1

Answer:

$f(x) =\frac{(2x+1)(x+0.5)}{2}$

Step-by-step explanation:

First, Kara walks straight East twice as much as Lindsay walks North. We are not given the actual number of miles, so if we call "x" the number of miles walked by Lindsay, Kara has walked twice that (2x) at the same time.

Then we need to add one mile to what Kara walked, and half a mile (0.5 mi) to what Lindsey walked. We represent the distances covered East and North from the campsite in the following sketch:

Notice also that we can create a right angle triangle by joining the end points were Kara and Lindsey are.

The area of such triangle (base x height)/2 using the actual lengths specified in the drawing gives:

$Area of triangle = \frac{(2x+1)(x+0.5)}{2}$