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

A. f(x) = x^2 + x + 0.25

Explanation:

Answer 2

A. f(x)=x^2+x+0.25

Explanation:

If x represents Lindsey's distance at 2:00 PM, then 2x represents Kara's distance at 2:00 PM because she walked twice as far as Lindsey. Then adding on the values we got for 2:30 PM, we get that Kara walked a distance of 2x+1 and Lindsey walked a distance of x+0.5 at the time of 2:30 PM. Now, we know that they have formed a right triangle because we are given the directions they walked in; east and north. This allows us to use a formula for the area of a right triangle: 1/2(L x W). Plugging in our values, we get...

1/2(2x+1)(x+0.5)

which simplifies to...

1/2(2x^2+2x+0.5)

which further simplifies to...

x^2+x+0.25

which is our answer.