ReasoningAbility.com

Distance Logic - Beginner-Intermediate Level: Pythagorean theorem BEGINNER-INTERMEDIATE

Ready to master distance logic? This benchmark test features 20 beginner-intermediate-level challenges. Worksheet 12 of 30 sharpens your Pythagorean theorem skills. Master distance measurement, relative distances, path length through guided practice. Perfect for developing test preparation.

📝 Worksheet 12 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 12 of 30 (40% complete)

Question 1

From point P, a person walks 8 m West, then 6 m South. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(8² + 6²)
3. = √(64 + 36) = √100 = 10 m
pythagoras, right-angle, shortest-distance

Question 2

Two persons A and B start from the same point. A walks 11 m West, then 9 m West. B walks 19 m South, then 14 m South, then 17 m West. What is the distance between them?
Step-by-step:
1. A's final position: (-20, 0)
2. B's final position: (-17, -33)
3. Distance = √[(-20--17)² + (0--33)²] = √[-3² + 33²] = 33 m
two-persons, relative, distance

Question 3

A person travels 7 m West, then 24 m South. Find the shortest distance from the starting point.
Step-by-step:
1. West and South are perpendicular directions
2. Shortest distance = √(7² + 24²) = √625 = 25 m
shortest-path, pythagoras

Question 4

A person walks 24 m North, then 10 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(24² + 10²) = √676 = 26 m
shortest-path, pythagoras

Question 5

A boat travels at 20 km/h in still water. The stream flows at 5 km/h. How long will it take to go 31 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 20 + 5 = 25 km/h
2. Time = Distance / Speed = 31 / 25 = 1.2 hours
boat, stream, upstream, downstream

Question 6

A 154 cm tall person casts a 284 cm shadow. A nearby building is 766 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 154/284 = 0.54
2. For object: Height / Shadow = 0.54
3. Shadow = Height / Ratio = 766 / 0.54 = 1412.6 cm
shadow, similar-triangles, ssc

Question 7

A person starts from point O and walks 5m East, then 13m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 5m East, then 13m North
2. Net position: (5, 13)
3. Distance = √(5² + 13²) = √194 = 14 m
basic, movement, straight-line

Question 8

A person walks from a point where his shadow length is measured to another point. The distances from a lamp post are 42 m and 79 m respectively. How far did he walk?
Step-by-step:
1. First position: distance from pole = 42 m
2. Second position: distance from pole = 79 m
3. Distance between positions = 79 - 42 = 37 m
shadow, similar-triangles, ssc

Question 9

Two runners start from the same point on a circular track of length 791 m. Their speeds are 10 m/s and 8 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |8 - 10| = 2 m/s
2. Time to meet = Track length / Relative speed = 791 / 2 = 395.5 seconds
circular, track, meeting, laps

Question 10

A boat travels 55 km downstream in 3.1 hours and upstream in 6.9 hours. The stream speed is 5 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 5 km/h
2. Downstream: 55/(x + 5) = 3.1
3. Upstream: 55/(x - 5) = 6.9
4. Solving gives x = 13 km/h
boat, stream, upstream, downstream

Question 11

A train 391 m long is running at 85 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 85 km/h = 23.6 m/s
2. Time = Length / Speed = 391 / 23.6 = 16.6 seconds
train, platform, pole, ssc

Question 12

Two persons A and B start from the same point. A walks 11 m East, then 10 m South. B walks 6 m West, then 11 m East. What is the distance between them?
Step-by-step:
1. A's final position: (11, -10)
2. B's final position: (5, 0)
3. Distance = √[(11-5)² + (-10-0)²] = √[6² + -10²] = 12 m
two-persons, relative, distance

Question 13

A boat travels 73 km downstream in 2.9 hours and upstream in 3.8 hours. The stream speed is 3 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 3 km/h
2. Downstream: 73/(x + 3) = 2.9
3. Upstream: 73/(x - 3) = 3.8
4. Solving gives x = 22 km/h
boat, stream, upstream, downstream

Question 14

A boat travels at 23 km/h in still water. The stream flows at 3 km/h. How long will it take to go 75 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 23 + 3 = 26 km/h
2. Time = Distance / Speed = 75 / 26 = 2.9 hours
boat, stream, upstream, downstream

Question 15

From point P, a person walks 15 m North, then 8 m East. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(15² + 8²)
3. = √(225 + 64) = √289 = 17 m
pythagoras, right-angle, shortest-distance

Question 16

Train A at 61 km/h and Train B at 54 km/h start from stations 535 km apart and move towards each other. How long will they take to meet?
Step-by-step:
1. Relative speed when moving towards each other = 61 + 54 = 115 km/h
2. Time = Distance / Relative Speed = 535 / 115 = 4.7 hours
relative, meeting, catch-up

Question 17

From point P, a person walks 7 m West, then 24 m South. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(7² + 24²)
3. = √(49 + 576) = √625 = 25 m
pythagoras, right-angle, shortest-distance

Question 18

A train 350 m long is running at 61 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 61 km/h = 16.9 m/s
2. Time = Length / Speed = 350 / 16.9 = 20.7 seconds
train, platform, pole, ssc

Question 19

Two runners start from the same point on a circular track of length 621 m. Their speeds are 12 m/s and 10 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 12 + 10 = 22 m/s
2. Time to meet = Track length / Relative speed = 621 / 22 = 28.2 seconds
circular, track, meeting, laps

Question 20

A person starts from point O and walks 18m North, then 18m South, then 21m South. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 18m North, then 18m South, then 21m South
2. Net position: (0, -21)
3. Distance = √(0² + -21²) = √441 = 21 m
basic, movement, straight-line
Previous Worksheet Next Worksheet