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Distance Logic - Intermediate-Advanced Level: relative distances INTERMEDIATE-ADVANCED

This fundamentals focus worksheet contains 20 intermediate-advanced-level distance logic problems. Worksheet 21 of 30 focuses on relative distances. Practice path length, position finding, coordinate geometry with our step-by-step solutions. Difficulty: advanced concepts with increasing complexity. Recommended for advanced developing learners.

📝 Worksheet 21 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 21 of 30 (70% complete)

Question 1

A boat travels at 14 km/h in still water. The stream flows at 4 km/h. How long will it take to go 42 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 14 - 4 = 10 km/h
2. Time = Distance / Speed = 42 / 10 = 4.2 hours
boat, stream, upstream, downstream

Question 2

A train 332 m long is running at 74 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 74 km/h = 20.6 m/s
2. Time = Length / Speed = 332 / 20.6 = 16.2 seconds
train, platform, pole, ssc

Question 3

A person walks 17 m North, then 19 m North, then 10 m South. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 26 m North
- East-West: 0 m 0
2. Displacement = √(0² + 26²) = √676 = 26 m
3. Total distance walked = 46 m
multi-stage, displacement, complex

Question 4

A train 271 m long is running at 89 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 89 km/h = 24.7 m/s
2. Time = Length / Speed = 271 / 24.7 = 11.0 seconds
train, platform, pole, ssc

Question 5

Two persons A and B start from the same point. A walks 16 m North, then 10 m East, then 5 m North. B walks 20 m South, then 12 m East. What is the distance between them?
Step-by-step:
1. A's final position: (10, 21)
2. B's final position: (12, -20)
3. Distance = √[(10-12)² + (21--20)²] = √[-2² + 41²] = 41 m
two-persons, relative, distance

Question 6

From point P, a person walks 15 m South, then 8 m West. 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 7

A person starts from point O and walks 14m West, then 17m East, then 9m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 14m West, then 17m East, then 9m East
2. Net position: (12, 0)
3. Distance = √(12² + 0²) = √144 = 12 m
basic, movement, straight-line

Question 8

From point P, a person walks 9 m East, then 12 m North. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(9² + 12²)
3. = √(81 + 144) = √225 = 15 m
pythagoras, right-angle, shortest-distance

Question 9

Two persons A and B start from the same point. A walks 7 m East, then 17 m North, then 12 m North. B walks 6 m West, then 14 m North. What is the distance between them?
Step-by-step:
1. A's final position: (7, 29)
2. B's final position: (-6, 14)
3. Distance = √[(7--6)² + (29-14)²] = √[13² + 15²] = 20 m
two-persons, relative, distance

Question 10

A train moves at 32 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 32 × 0.5 = 16.0 km
speed, time, basic

Question 11

Two persons A and B start from the same point. A walks 6 m North, then 11 m West. B walks 19 m North, then 13 m West, then 17 m West. What is the distance between them?
Step-by-step:
1. A's final position: (-11, 6)
2. B's final position: (-30, 19)
3. Distance = √[(-11--30)² + (6-19)²] = √[19² + -13²] = 23 m
two-persons, relative, distance

Question 12

A train 207 m long is running at 89 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 89 km/h = 24.7 m/s
2. Time = Length / Speed = 207 / 24.7 = 8.4 seconds
train, platform, pole, ssc

Question 13

Car A at 49 km/h and Car B at 78 km/h start from the same point in the same direction. How long will it take for them to be 326 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |78 - 49| = 29 km/h
2. Time = Distance / Relative Speed = 326 / 29 = 11.2 hours
3. The second car will be 326 km ahead after 11.2 hours
relative, meeting, catch-up

Question 14

A runner runs at 10 m/s on a circular track of length 753 m for 98 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 98 seconds = 10 × 98 = 980 m
2. Number of laps = Distance / Track length = 980 / 753 = 1.3 laps
circular, track, meeting, laps

Question 15

A person starts from point O and walks 13m East, then 21m East, then 10m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 13m East, then 21m East, then 10m West
2. Net position: (24, 0)
3. Distance = √(24² + 0²) = √576 = 24 m
basic, movement, straight-line

Question 16

A train 211 m long is running at 86 km/h. How long will it take to cross a 234 m long platform?
Step-by-step:
1. Speed = 86 km/h = 23.9 m/s
2. Total distance = Train length + Platform length = 211 + 234 = 445 m
3. Time = Distance / Speed = 445 / 23.9 = 18.6 seconds
train, platform, pole, ssc

Question 17

Train A at 64 km/h and Train B at 61 km/h start from stations 440 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 = 64 + 61 = 125 km/h
2. Time = Distance / Relative Speed = 440 / 125 = 3.5 hours
relative, meeting, catch-up

Question 18

Train A at 64 km/h and Train B at 80 km/h start from stations 504 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 = 64 + 80 = 144 km/h
2. Time = Distance / Relative Speed = 504 / 144 = 3.5 hours
relative, meeting, catch-up

Question 19

A person walks 16 m West, then 18 m North, then 18 m North, then 12 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 48 m North
- East-West: -16 m West
2. Displacement = √(-16² + 48²) = √2560 = 51 m
3. Total distance walked = 64 m
multi-stage, displacement, complex

Question 20

Two persons A and B start from the same point. A walks 18 m East, then 17 m East. B walks 17 m South, then 15 m South, then 6 m North. What is the distance between them?
Step-by-step:
1. A's final position: (35, 0)
2. B's final position: (0, -26)
3. Distance = √[(35-0)² + (0--26)²] = √[35² + 26²] = 44 m
two-persons, relative, distance
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