Question

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question 3 (1 point)
some hikers travel 2 km north, turn toward the west and travel 4km, turn toward the south and travel 6 km, then finally travel east for 4 km. what is their distance?
a 12km
b 6km
c 4km s
d 16km

Explanation:

Step1: Identify the type of distance

The problem is asking for the total distance traveled, which is the sum of all the individual segments of the journey.

Step2: Sum the distances

The hikers travel 2 km north, 4 km west, 6 km south, and 4 km east. To find the total distance, we add these lengths together:
\[
2 + 4 + 6 + 4
\]
First, add 2 and 4: \(2 + 4 = 6\)
Then, add 6 (from the previous sum) and 6: \(6 + 6 = 12\)
Then, add 12 and 4: \(12 + 4 = 16\)? Wait, no, wait. Wait, maybe I misread. Wait, no, the options have 12km as option a. Wait, let's recalculate: 2 (north) + 4 (west) + 6 (south) + 4 (east). So 2 + 4 is 6, 6 + 6 is 12, 12 + 4 is 16? But option a is 12km, option d is 16km. Wait, maybe the question is about displacement? But no, the question says "distance", which is the total path length. Wait, let's check again.

Wait, the problem says "What is their distance?" – distance traveled is the sum of all the paths. So 2 + 4 + 6 + 4 = 16? But option d is 16km. Wait, but maybe I made a mistake. Wait, let's check the options again. The options are:

a. 12km

b. 6km

c. 4km S

d. 16km

Wait, maybe the question was supposed to be displacement? But no, distance is total path. Wait, let's recalculate: 2 (north) + 4 (west) + 6 (south) + 4 (east). So 2 + 4 = 6, 6 + 6 = 12, 12 + 4 = 16. So the total distance is 16km, which is option d. But wait, maybe I misread the problem. Let me check again.

Wait, the problem says: "Some hikers travel 2 km north, turn toward the west and travel 4km, turn toward the south and travel 6 km, then finally travel east for 4 km. What is their distance?"

So distance is the sum of all the movements: 2 + 4 + 6 + 4 = 16 km. So the answer should be d. 16km.

Wait, but maybe the question was about displacement? Let's check displacement. Displacement is the straight-line distance from start to end. Let's calculate that.

North: 2 km, then south: 6 km. So net north-south displacement: 2 - 6 = -4 km (4 km south).

West: 4 km, then east: 4 km. So net east-west displacement: 4 - 4 = 0 km.

So displacement is 4 km south. But that's option c. But the question says "distance", not "displacement". So maybe there's a mistake in the problem, or maybe I misread.

Wait, the original problem: "What is their distance?" – distance traveled is the total path, so 2 + 4 + 6 + 4 = 16 km. So option d.

But let's confirm:

2 km north: distance += 2

4 km west: distance += 4 (total 6)

6 km south: distance += 6 (total 12)

4 km east: distance += 4 (total 16)

Yes, so total distance is 16 km, which is option d.

Answer:

d. 16km