Question

7. Jared the Joker hiked 10 miles north, 11 miles west, 2 miles south and 4 miles west and then returned via a straight route back to his starting point. How far did Jared hike in all?

a. 54 mi. b. 42 mi. c. 44 mi. d. 40 mi. e. 46 mi.​

Answer 1

Jared hiked a total distance of 27 miles, but his displacement is 0 miles. Therefore, the correct answer is 40 mi.

Step-by-step explanation:

To find out how far Jared hiked in total, we need to calculate the total distance traveled in each direction and then find the total displacement by adding up the distances in each direction.

First, let's calculate the distances. Jared hiked 10 miles north, 11 miles west, 2 miles south, and 4 miles west. In total, he hiked 10 + 11 + 2 + 4 = 27 miles.

Next, let's calculate the displacement. Displacement is the straight-line distance between the starting point and the ending point. Since Jared ended up at his starting point, his displacement is 0 miles. Therefore, the correct answer is d. 40 mi.

Answer 2

c. 44 mi.

Step-by-step explanation:

To solve for the total distance hiked by Jared, we need to add all the given distance and with the distance when he returned to the starting point.

Use the illustration below for reference.

The last point given and the starting point forms a right triangle. We can then use Pythagorean theorem on this case.

The right triangle formed has legs of 8 mi (10mi - 2mi) and 15 mi (4mi + 11mi).

c² = a² + b²

where a and b are the legs of the triangle and c is the hypotenuse.

Based on the illustration, a and b are 8mi and 15mi while c is represented as d

Let's solve!

c² = a² + b²

d² = (8mi)² + (15mi)²

d² = 64 mi² + 225 mi²

d² = 289 mi²

Extract the square root on both sides of the equation

d = 17 mi

Add all the given distance by 17 mi

Total distance = 10mi + 11mi + 2mi + 4 mi + 17 mi

Total distance = 44 mi