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Distance Logic - Expert Level: grid distances EXPERT

Strategic basic drills ★ for distance logic: 20 expert-level problems. Worksheet 29 of 30 - Focus: grid distances. Develop expertise in distance calculation, shortest path, displacement problems with step-by-step solutions. Ideal for expert-level learners targeting challenging problems and time-bound practice.

📝 Worksheet 29 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 29 of 30 (96% complete)

Question 1

A train 203 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 = 203 / 13.9 = 14.6 seconds
train, platform, pole, ssc

Question 2

From point P, a person walks 20 m North, then 21 m East. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(20² + 21²)
3. = √(400 + 441) = √841 = 29 m
pythagoras, right-angle, shortest-distance

Question 3

A person walks from a point where his shadow length is measured to another point. The distances from a lamp post are 31 m and 98 m respectively. How far did he walk?
Step-by-step:
1. First position: distance from pole = 31 m
2. Second position: distance from pole = 98 m
3. Distance between positions = 98 - 31 = 67 m
shadow, similar-triangles, ssc

Question 4

A person travels 8 m West, then 6 m South. Find the shortest distance from the starting point.
Step-by-step:
1. West and South are perpendicular directions
2. Shortest distance = √(8² + 6²) = √100 = 10 m
shortest-path, pythagoras

Question 5

A train moves at 37 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 37 × 0.5 = 18.5 km
speed, time, basic

Question 6

Two persons A and B start from the same point. A walks 20 m East, then 13 m North, then 7 m East. B walks 13 m East, then 16 m South. What is the distance between them?
Step-by-step:
1. A's final position: (27, 13)
2. B's final position: (13, -16)
3. Distance = √[(27-13)² + (13--16)²] = √[14² + 29²] = 32 m
two-persons, relative, distance

Question 7

A train 233 m long is running at 47 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 47 km/h = 13.1 m/s
2. Time = Length / Speed = 233 / 13.1 = 17.8 seconds
train, platform, pole, ssc

Question 8

Two runners start from the same point on a circular track of length 457 m. Their speeds are 5 m/s and 13 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |13 - 5| = 8 m/s
2. Time to meet = Track length / Relative speed = 457 / 8 = 57.1 seconds
circular, track, meeting, laps

Question 9

Two persons A and B start from the same point. A walks 13 m South, then 16 m West, then 8 m North. B walks 18 m East, then 15 m North, then 8 m West. What is the distance between them?
Step-by-step:
1. A's final position: (-16, -5)
2. B's final position: (10, 15)
3. Distance = √[(-16-10)² + (-5-15)²] = √[-26² + -20²] = 33 m
two-persons, relative, distance

Question 10

A train moves at 52 km/h for 45 minutes. What distance does it cover?
Time = 45 minutes = 0.75 hours
Distance = 52 × 0.75 = 39.0 km
speed, time, basic

Question 11

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 12

A person walks 10 m South, then 15 m North, then 20 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 5 m North
- East-West: -20 m West
2. Displacement = √(-20² + 5²) = √425 = 21 m
3. Total distance walked = 45 m
multi-stage, displacement, complex

Question 13

A 169 cm tall person casts a 185 cm shadow. A nearby building is 725 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 169/185 = 0.91
2. For object: Height / Shadow = 0.91
3. Shadow = Height / Ratio = 725 / 0.91 = 793.6 cm
shadow, similar-triangles, ssc

Question 14

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 15

A car travels at 69 km/h for 5 hours. What distance does it cover?
Distance = Speed × Time = 69 × 5 = 345 km
speed, time, basic

Question 16

A boat travels 53 km downstream in 2.8 hours and upstream in 17.7 hours. The stream speed is 8 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 8 km/h
2. Downstream: 53/(x + 8) = 2.8
3. Upstream: 53/(x - 8) = 17.7
4. Solving gives x = 11 km/h
boat, stream, upstream, downstream

Question 17

Two runners start from the same point on a circular track of length 649 m. Their speeds are 6 m/s and 10 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |10 - 6| = 4 m/s
2. Time to meet = Track length / Relative speed = 649 / 4 = 162.2 seconds
circular, track, meeting, laps

Question 18

Train A at 50 km/h and Train B at 68 km/h start from stations 457 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 = 50 + 68 = 118 km/h
2. Time = Distance / Relative Speed = 457 / 118 = 3.9 hours
relative, meeting, catch-up

Question 19

A person starts from point O and walks 9m West, then 22m West, then 9m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 9m West, then 22m West, then 9m West
2. Net position: (-40, 0)
3. Distance = √(-40² + 0²) = √1600 = 40 m
basic, movement, straight-line

Question 20

A person travels from A to B at 33 km/h and returns at 43 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 × 33 × 43) / (33 + 43)
3. = 2838 / 76 = 37.3 km/h
average, speed, distance
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