Question

100 POINTS! You and a friend are hiking and find yourselves near the top of a waterfall. There is a path to hike down that takes 1.8 miles to reach the bottom safely and go swimming. There is also a path that is 1.3 miles down to a great place to eat lunch. Your friend wants to stay at the top of the waterfall and fly his drone overhead to take pictures from the sky. A drone is a flying robot that can be remotely controlled with computer software or technology. Draw a vertical number line to help you answer the questions.

Part A: How far would the drone need to fly up in the air to be the opposite distance from you when you are eating lunch? (3 points)

Part B: How far would the drone need to fly up in the air to be the opposite distance from you when you are swimming? (3 points)

Part C: What does the value of zero represent in this problem? (3 points)

Part D: Use absolute value to show that if you hike down to go swimming and then hike back to the top to meet your friend that you hiked the same distance in both directions. (3 points)

Answer 1

Part A

The vertical number line would represent the height above ground level.

The total distance of the waterfall is:

• 1.8 + 1.3 = 3.1 miles

So, the opposite distance from where you are eating lunch would be:

• 3.1 - 1.3 = 1.8 miles

Therefore, the drone would need to fly up 1.8 miles in the air..

Part B

Similarly, to find the opposite distance from where you are swimming, we need to subtract the distance of the path to the bottom from the total distance of the waterfall.

So, the opposite distance from where you are swimming would be:

• 3.1 - 1.8 = 1.3 miles

Part C

In this problem, the value of zero represents the top of the waterfall where you and your friend are currently standing.

Part D

Let's say the distance from the top of the waterfall to the bottom is d miles. So, the total distance you hike to reach the bottom and then back to the top would be 2d miles.

Now, if you hike down to go swimming, the absolute value of the distance you cover would be |d|.

And if you hike back to the top, the absolute value of the distance you cover would be |-d| = |d|.

Since both distances are equal, we can say that you hiked the same distance in both directions.