Question

Malcolm sets out in a giant blizzard so thick he can't see his own boots. He uses his compass to try to find his buried food stash, heading 1 km East, then 4 km South, then 3 km East. He then pitches a tent. How far is he from his original location in meters?

Option 1: 3,000 meters
Option 2: 5,000 meters
Option 3: 5,830 meters
Option 4: 7,000 meters

Answer 1

Malcolm's final position is approximately 5,660 meters from his starting point after traveling east and south, forming a right-angled triangle. The nearest correct option is 5,000 meters, as calculated using the Pythagorean theorem.

Step-by-step explanation:

The question asks how far Malcolm is from his original location after traveling 1 km East, then 4 km South, and finally 3 km East again. To solve this, we can visualize or draw the path Malcolm took and then use the Pythagorean theorem to calculate the direct distance from his starting point to his final location.

First, he moves 1 km East and then 3 km East, which sums up to 4 km East in total. Next, he moves 4 km South. These two movements form a right-angled triangle with the legs being 4 km East and 4 km South.

Using the Pythagorean theorem:

a² + b² = c²
c = √(a² + b²)

where a is the total distance East (4 km) and b is the distance South (4 km). Plugging these into the equation gives us:

c = √(4² + 4²)
c = √(16 + 16)
c = √(32)
c ≈ 5.66 km

Since 1 km is equal to 1,000 meters, Malcolm's final position is approximately 5,660 meters from his original location. Thus, Option 2: 5,000 meters is the nearest correct option provided, though it is slightly less than the calculated distance.