Find the distance (Algebra)

Question

Steve and Tammy leave a campground, hiking on two different trails. Steve heads south and Tammy heads east. By lunchtime they are 6 mi apart. Tammy walked 2 miles more than Steve. Find the distance each person hiked. Use completing the square to find your answer rounded to the nearest tenth of a mile.

This is a 10-point question so make sure you are showing ALL steps. You will not be granted a redo if your work is lacking.

Answer 1

Hi Taylor,

 

Let the distance Steve walked be x mi. Then, the distance Tammy walked is x+2 mi.

 

Now we have a right triangle whose hypotenuse is 6 and the legs are x and x+2. We can use the Pythagorean Theorem to find x.

x^2 + (x+2)^2 = 6^2

x^2 + x^2 + 4x + 4 = 36

2x^2 + 4x = 32

To complete the square, the leading coefficient needs to be 1 so divide by 2.

x^2 + 2x = 16

Then, we need to add (b/2)^2 to both sides. b = 2

x^2 + 2x + (2/2)^2 = 16 + (2/2)^2

x^2 + 2x + 1 = 16 + 1

(x + 1)^2 = 17

x + 1 = sqrt(17)

x = 3.1 mi This is the distance Steve walked.

3.1 + 2 = 5.1 mi This is the distance Tammy hiked.