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Distance Logic - Intermediate Level: shortest path INTERMEDIATE

Quick mental agility ★ session: 20 intermediate-level distance logic questions. Worksheet 17 of 30 - Focus: shortest path. Practice displacement problems, route mapping, distance measurement with instant feedback. Great for mid-level students needing moderate complexity with mixed patterns practice.

📝 Worksheet 17 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 17 of 30 (56% complete)

Question 1

A person walks 15 m North, then 20 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(15² + 20²) = √625 = 25 m
shortest-path, pythagoras

Question 2

A person starts from point O and walks 21m South, then 25m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 21m South, then 25m North
2. Net position: (0, 4)
3. Distance = √(0² + 4²) = √16 = 4 m
basic, movement, straight-line

Question 3

Train A at 62 km/h and Train B at 50 km/h start from stations 549 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 = 62 + 50 = 112 km/h
2. Time = Distance / Relative Speed = 549 / 112 = 4.9 hours
relative, meeting, catch-up

Question 4

From point P, a person walks 5 m West, then 12 m South. 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 5

Train A at 43 km/h and Train B at 71 km/h start from stations 509 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 = 43 + 71 = 114 km/h
2. Time = Distance / Relative Speed = 509 / 114 = 4.5 hours
relative, meeting, catch-up

Question 6

A person starts from point O and walks 7m East, then 9m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 7m East, then 9m East
2. Net position: (16, 0)
3. Distance = √(16² + 0²) = √256 = 16 m
basic, movement, straight-line

Question 7

A train 270 m long is running at 84 km/h. How long will it take to cross a 199 m long platform?
Step-by-step:
1. Speed = 84 km/h = 23.3 m/s
2. Total distance = Train length + Platform length = 270 + 199 = 469 m
3. Time = Distance / Speed = 469 / 23.3 = 20.1 seconds
train, platform, pole, ssc

Question 8

A train 231 m long is running at 49 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 49 km/h = 13.6 m/s
2. Time = Length / Speed = 231 / 13.6 = 17.0 seconds
train, platform, pole, ssc

Question 9

A train 192 m long is running at 63 km/h. How long will it take to cross a 179 m long platform?
Step-by-step:
1. Speed = 63 km/h = 17.5 m/s
2. Total distance = Train length + Platform length = 192 + 179 = 371 m
3. Time = Distance / Speed = 371 / 17.5 = 21.2 seconds
train, platform, pole, ssc

Question 10

A train 324 m long is running at 70 km/h. How long will it take to cross a 261 m long platform?
Step-by-step:
1. Speed = 70 km/h = 19.4 m/s
2. Total distance = Train length + Platform length = 324 + 261 = 585 m
3. Time = Distance / Speed = 585 / 19.4 = 30.1 seconds
train, platform, pole, ssc

Question 11

A 165 cm tall person casts a 108 cm shadow. A nearby building is 889 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 165/108 = 1.53
2. For object: Height / Shadow = 1.53
3. Shadow = Height / Ratio = 889 / 1.53 = 581.9 cm
shadow, similar-triangles, ssc

Question 12

A train 291 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 = 291 / 20.6 = 14.2 seconds
train, platform, pole, ssc

Question 13

Two runners start from the same point on a circular track of length 671 m. Their speeds are 11 m/s and 9 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 11 + 9 = 20 m/s
2. Time to meet = Track length / Relative speed = 671 / 20 = 33.5 seconds
circular, track, meeting, laps

Question 14

Train A at 62 km/h and Train B at 71 km/h start from stations 547 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 = 62 + 71 = 133 km/h
2. Time = Distance / Relative Speed = 547 / 133 = 4.1 hours
relative, meeting, catch-up

Question 15

Train A at 66 km/h and Train B at 54 km/h start from stations 361 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 = 66 + 54 = 120 km/h
2. Time = Distance / Relative Speed = 361 / 120 = 3.0 hours
relative, meeting, catch-up

Question 16

A person walks 9 m North, then 12 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(9² + 12²) = √225 = 15 m
shortest-path, pythagoras

Question 17

Two runners start from the same point on a circular track of length 736 m. Their speeds are 10 m/s and 9 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 10 + 9 = 19 m/s
2. Time to meet = Track length / Relative speed = 736 / 19 = 38.7 seconds
circular, track, meeting, laps

Question 18

Two runners start from the same point on a circular track of length 698 m. Their speeds are 5 m/s and 9 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 5 + 9 = 14 m/s
2. Time to meet = Track length / Relative speed = 698 / 14 = 49.9 seconds
circular, track, meeting, laps

Question 19

Car A at 51 km/h and Car B at 72 km/h start from the same point in the same direction. How long will it take for them to be 522 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |72 - 51| = 21 km/h
2. Time = Distance / Relative Speed = 522 / 21 = 24.9 hours
3. The second car will be 522 km ahead after 24.9 hours
relative, meeting, catch-up

Question 20

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
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