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Question 1 / 7
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1
A person walks 5 km south, then 3 km west, and finally 5 km north. What is the final direction from the starting point?
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Solution: Step 1: Break down the movements - 5 km south, then 3 km right (west), then 5 km left (north). Step 2: The south and north movements cancel out 5 km each. Step 3: The person ends up 3 km west of the original starting point. Step 4: Determine the direction based on the final position.
2
A person is standing in a group with a certain number of people to his right and left. If there are 3 people to his right and 4 people to his left, what is the total number of people in the group?
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Solution: Step 1: Identify the number of people to the right and left of the central person. Step 2: Add the people to the right, left, and the central person. Step 3: Calculate the total number of people: 3 (right) + 1 (central) + 4 (left) = 8 people. The correct answer is 8.
3
A student goes astray on the way home from school. He walks 3km south, then 5km east, then 3km north, and finally 2km west. What is the distance between his school and home?
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Solution: Step 1: Visualize the movements - The student moves 3km south, then 5km east, then 3km north, and 2km west. Step 2: Calculate the net displacement in the north-south direction - 3km south - 3km north = 0km. Step 3: Calculate the net displacement in the east-west direction - 5km east - 2km west = 3km east. Step 4: Determine the distance between school and home - The distance is the net eastward movement, which is 3km.
4
An individual starts at point A, walks 10m north to point B, then 6m west to point C, followed by 7m north to point D, then 10m east to point E, and finally 7m south to point F. Determine the direction of point D relative to point F.
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Solution: Step 1: Analyze movements from A to F - North from A to B: 10m - West to C: 6m - North to D: 7m - East to E: 10m - South to F: 7m Step 2: Calculate net displacement in north-south direction - North: 10m (to B) + 7m (to D) = 17m - South: 7m (to F) - Net northward displacement: 17m - 7m = 10m Step 3: Calculate net displacement in east-west direction - West: 6m (to C) - East: 10m (to E) - Net eastward displacement: 10m - 6m = 4m Step 4: Determine direction of D from F - D is 10m north and 4m west of F - Hence, D is northwest of F
5
A person walks 2m east, then 7m south, then 5m east, then 7m south, and finally 1m west. What is the total distance from the starting point?
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Solution: Step 1: Break down the movements into components - East-west movement: 2m east + 5m east - 1m west = 6m east - North-south movement: 7m south + 7m south = 14m south Step 2: Use Pythagoras theorem to find distance from starting point Distance = sqrt((6m)^2 + (14m)^2) = sqrt(36 + 196) = sqrt(232) = sqrt(4*58) = 2*sqrt(58) = 8m (approx) However, exact calculation yields: Distance = sqrt(6^2 + 14^2) = sqrt(36+196) = sqrt(232) The movements result in 6m east and 14m south. By visual analysis and Pythagoras, we find the distance is √(6^2+14^2) = √232 = 8m.
6
A person walks 35m west, then 15m north, then 20m east, and finally 15m south. What is the distance from the starting point?
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Solution: Step 1: Break down the movements into components. Step 2: West-East movement: 35m west - 20m east = 15m west. Step 3: North-South movement: 15m north - 15m south = 0m. Step 4: Since there's no net North-South displacement, the final position is 15m west of the starting point. Step 5: Therefore, the distance from the starting point is 15m.
7
A person walks 25m North, then turns left and walks 30m, and finally turns left again and walks 25m. How far and in which direction is the person from the starting position?
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Solution: Step 1: Visualize the movements. - Walk 25m North - Turn left and walk 30m West - Turn left and walk 25m South Step 2: Determine the net displacement. North-South movement: 25m North - 25m South = 0m East-West movement: 30m West Step 3: Conclude the final position. The person ends up 30m to the West of the starting position. Step 4: Verify the answer. The correct answer is indeed 30m to the West.
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