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Distance Logic - Intermediate Level: distance calculation INTERMEDIATE

Master distance logic concepts through this excellence pursuit practice set. Worksheet 16 of 30 contains 20 intermediate-level problems. Deep dive into distance calculation while learning shortest path, displacement problems, route mapping. Recommended for mid-level learners aiming for moderate complexity with mixed patterns.

📝 Worksheet 16 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 16 of 30 (53% complete)

Question 1

From point P, a person walks 5 m South, then 12 m West. 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 2

A person walks 8 m North, then 6 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(8² + 6²) = √100 = 10 m
shortest-path, pythagoras

Question 3

A person starts from point O and walks 21m South, then 9m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 21m South, then 9m East
2. Net position: (9, -21)
3. Distance = √(9² + -21²) = √522 = 23 m
basic, movement, straight-line

Question 4

A boat travels at 21 km/h in still water. The stream flows at 8 km/h. How long will it take to go 78 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 21 - 8 = 13 km/h
2. Time = Distance / Speed = 78 / 13 = 6.0 hours
boat, stream, upstream, downstream

Question 5

A train moves at 64 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 64 × 0.25 = 16.0 km
speed, time, basic

Question 6

A runner runs at 10 m/s on a circular track of length 604 m for 71 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 71 seconds = 10 × 71 = 710 m
2. Number of laps = Distance / Track length = 710 / 604 = 1.2 laps
circular, track, meeting, laps

Question 7

Train A at 62 km/h and Train B at 73 km/h start from stations 308 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 + 73 = 135 km/h
2. Time = Distance / Relative Speed = 308 / 135 = 2.3 hours
relative, meeting, catch-up

Question 8

Car A at 47 km/h and Car B at 59 km/h start from the same point in the same direction. How long will it take for them to be 379 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |59 - 47| = 12 km/h
2. Time = Distance / Relative Speed = 379 / 12 = 31.6 hours
3. The second car will be 379 km ahead after 31.6 hours
relative, meeting, catch-up

Question 9

A person walks 18 m North, then 13 m West, then 8 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 18 m North
- East-West: -21 m West
2. Displacement = √(-21² + 18²) = √765 = 28 m
3. Total distance walked = 39 m
multi-stage, displacement, complex

Question 10

A train 293 m long is running at 77 km/h. How long will it take to cross a 170 m long platform?
Step-by-step:
1. Speed = 77 km/h = 21.4 m/s
2. Total distance = Train length + Platform length = 293 + 170 = 463 m
3. Time = Distance / Speed = 463 / 21.4 = 21.6 seconds
train, platform, pole, ssc

Question 11

Two runners start from the same point on a circular track of length 633 m. Their speeds are 5 m/s and 12 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 5 + 12 = 17 m/s
2. Time to meet = Track length / Relative speed = 633 / 17 = 37.2 seconds
circular, track, meeting, laps

Question 12

A person starts from point O and walks 23m North, then 15m South, then 22m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 23m North, then 15m South, then 22m East
2. Net position: (22, 8)
3. Distance = √(22² + 8²) = √548 = 23 m
basic, movement, straight-line

Question 13

A person walks 16 m West, then 24 m South, then 19 m South, then 25 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -43 m South
- East-West: -41 m West
2. Displacement = √(-41² + -43²) = √3530 = 59 m
3. Total distance walked = 84 m
multi-stage, displacement, complex

Question 14

Two persons A and B start from the same point. A walks 16 m West, then 17 m South. B walks 14 m West, then 15 m North. What is the distance between them?
Step-by-step:
1. A's final position: (-16, -17)
2. B's final position: (-14, 15)
3. Distance = √[(-16--14)² + (-17-15)²] = √[-2² + -32²] = 32 m
two-persons, relative, distance

Question 15

Car A at 45 km/h and Car B at 57 km/h start from the same point in the same direction. How long will it take for them to be 497 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |57 - 45| = 12 km/h
2. Time = Distance / Relative Speed = 497 / 12 = 41.4 hours
3. The second car will be 497 km ahead after 41.4 hours
relative, meeting, catch-up

Question 16

A boat travels at 11 km/h in still water. The stream flows at 5 km/h. How long will it take to go 37 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 11 - 5 = 6 km/h
2. Time = Distance / Speed = 37 / 6 = 6.2 hours
boat, stream, upstream, downstream

Question 17

A person travels at 48 km/h for 2 hours and then at 75 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (48 + 75) / 2 = 61.5 km/h
average, speed, distance

Question 18

A car travels at 56 km/h for 2 hours. What distance does it cover?
Distance = Speed × Time = 56 × 2 = 112 km
speed, time, basic

Question 19

Two persons A and B start from the same point. A walks 7 m East, then 20 m North, then 16 m East. B walks 17 m South, then 14 m South, then 16 m West. What is the distance between them?
Step-by-step:
1. A's final position: (23, 20)
2. B's final position: (-16, -31)
3. Distance = √[(23--16)² + (20--31)²] = √[39² + 51²] = 64 m
two-persons, relative, distance

Question 20

A person walks from a point where his shadow length is measured to another point. The distances from a lamp post are 27 m and 76 m respectively. How far did he walk?
Step-by-step:
1. First position: distance from pole = 27 m
2. Second position: distance from pole = 76 m
3. Distance between positions = 76 - 27 = 49 m
shadow, similar-triangles, ssc
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