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Distance Logic - Beginner Level: distance calculation BEGINNER

This foundation builder 🌟 worksheet contains 20 beginner-level distance logic problems. Worksheet 1 of 30 focuses on distance calculation. Practice distance calculation, shortest path, displacement problems with our step-by-step solutions. Difficulty: foundational concepts and basic patterns. Recommended for entry-level learners.

📝 Worksheet 1 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 1 of 30 (3% complete)

Question 1

From point X, a person goes 5 m East, then 12 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(5² + 12²) = √169 = 13 m
shortest-path, pythagoras

Question 2

From point X, a person goes 3 m East, then 4 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(3² + 4²) = √25 = 5 m
shortest-path, pythagoras

Question 3

Two persons A and B start from the same point. A walks 14 m West, then 9 m South, then 12 m East. B walks 19 m West, then 20 m West, then 11 m East. What is the distance between them?
Step-by-step:
1. A's final position: (-2, -9)
2. B's final position: (-28, 0)
3. Distance = √[(-2--28)² + (-9-0)²] = √[26² + -9²] = 28 m
two-persons, relative, distance

Question 4

A person starts from point O and walks 8m West, then 21m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 8m West, then 21m East
2. Net position: (13, 0)
3. Distance = √(13² + 0²) = √169 = 13 m
basic, movement, straight-line

Question 5

A person walks 18 m East, then 16 m East, then 13 m South, then 20 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -13 m South
- East-West: 14 m East
2. Displacement = √(14² + -13²) = √365 = 19 m
3. Total distance walked = 67 m
multi-stage, displacement, complex

Question 6

A person travels at 33 km/h for 2 hours and then at 49 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (33 + 49) / 2 = 41.0 km/h
average, speed, distance

Question 7

A boat travels at 21 km/h in still water. The stream flows at 6 km/h. How long will it take to go 52 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 21 + 6 = 27 km/h
2. Time = Distance / Speed = 52 / 27 = 1.9 hours
boat, stream, upstream, downstream

Question 8

A car travels at 30 km/h for 4 hours. What distance does it cover?
Distance = Speed × Time = 30 × 4 = 120 km
speed, time, basic

Question 9

A 157 cm tall person casts a 212 cm shadow. A nearby building is 991 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 157/212 = 0.74
2. For object: Height / Shadow = 0.74
3. Shadow = Height / Ratio = 991 / 0.74 = 1338.2 cm
shadow, similar-triangles, ssc

Question 10

A train 392 m long is running at 50 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 50 km/h = 13.9 m/s
2. Time = Length / Speed = 392 / 13.9 = 28.2 seconds
train, platform, pole, ssc

Question 11

A person starts from point O and walks 5m North, then 14m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 5m North, then 14m West
2. Net position: (-14, 5)
3. Distance = √(-14² + 5²) = √221 = 15 m
basic, movement, straight-line

Question 12

From point P, a person walks 5 m North, then 12 m East. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(5² + 12²)
3. = √(25 + 144) = √169 = 13 m
pythagoras, right-angle, shortest-distance

Question 13

A boat travels at 11 km/h in still water. The stream flows at 7 km/h. How long will it take to go 70 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 11 + 7 = 18 km/h
2. Time = Distance / Speed = 70 / 18 = 3.9 hours
boat, stream, upstream, downstream

Question 14

A car travels at 51 km/h for 6 hours. What distance does it cover?
Distance = Speed × Time = 51 × 6 = 306 km
speed, time, basic

Question 15

From point P, a person walks 3 m West, then 4 m South. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(3² + 4²)
3. = √(9 + 16) = √25 = 5 m
pythagoras, right-angle, shortest-distance

Question 16

A 174 cm tall person casts a 212 cm shadow. A building casts a 570 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 212/174 = 1.22
2. For object: Shadow / Height = 1.22
3. Height = Shadow / Ratio = 570 / 1.22 = 467.8 cm
shadow, similar-triangles, ssc

Question 17

A person travels from A to B at 59 km/h and returns at 75 km/h. What is the average speed for the entire journey?
Step-by-step:
1. For equal distances, Average Speed = (2 × v1 × v2) / (v1 + v2)
2. = (2 × 59 × 75) / (59 + 75)
3. = 8850 / 134 = 66.0 km/h
average, speed, distance

Question 18

From point X, a person goes 7 m East, then 24 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(7² + 24²) = √625 = 25 m
shortest-path, pythagoras

Question 19

Two runners start from the same point on a circular track of length 543 m. Their speeds are 7 m/s and 12 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |12 - 7| = 5 m/s
2. Time to meet = Track length / Relative speed = 543 / 5 = 108.6 seconds
circular, track, meeting, laps

Question 20

A person starts from point O and walks 13m North, then 18m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 13m North, then 18m West
2. Net position: (-18, 13)
3. Distance = √(-18² + 13²) = √493 = 22 m
basic, movement, straight-line
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