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Distance Logic - Beginner Level: route mapping BEGINNER

Level up your distance logic skills with this entry level practice. 20 beginner-level problems await in Worksheet 4 of 30. Focus area: route mapping. Learn route mapping, distance measurement, relative distances through systematic practice. Designed for entry-level learners seeking foundational concepts and basic patterns.

📝 Worksheet 4 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 4 of 30 (13% complete)

Question 1

A boat travels 62 km downstream in 2.3 hours and upstream in 3.0 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: 62/(x + 3) = 2.3
3. Upstream: 62/(x - 3) = 3.0
4. Solving gives x = 24 km/h
boat, stream, upstream, downstream

Question 2

A person starts from point O and walks 11m West, then 12m South. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 11m West, then 12m South
2. Net position: (-11, -12)
3. Distance = √(-11² + -12²) = √265 = 16 m
basic, movement, straight-line

Question 3

A person starts from point O and walks 16m West, then 20m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 16m West, then 20m West
2. Net position: (-36, 0)
3. Distance = √(-36² + 0²) = √1296 = 36 m
basic, movement, straight-line

Question 4

A train moves at 32 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 32 × 0.25 = 8.0 km
speed, time, basic

Question 5

A boat travels at 21 km/h in still water. The stream flows at 7 km/h. How long will it take to go 47 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 21 + 7 = 28 km/h
2. Time = Distance / Speed = 47 / 28 = 1.7 hours
boat, stream, upstream, downstream

Question 6

A train 289 m long is running at 58 km/h. How long will it take to cross a 135 m long platform?
Step-by-step:
1. Speed = 58 km/h = 16.1 m/s
2. Total distance = Train length + Platform length = 289 + 135 = 424 m
3. Time = Distance / Speed = 424 / 16.1 = 26.3 seconds
train, platform, pole, ssc

Question 7

A person walks 14 m South, then 19 m East, then 21 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -14 m South
- East-West: -2 m West
2. Displacement = √(-2² + -14²) = √200 = 14 m
3. Total distance walked = 54 m
multi-stage, displacement, complex

Question 8

A 164 cm tall person casts a 228 cm shadow. A building casts a 574 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 228/164 = 1.39
2. For object: Shadow / Height = 1.39
3. Height = Shadow / Ratio = 574 / 1.39 = 412.9 cm
shadow, similar-triangles, ssc

Question 9

Two persons A and B start from the same point. A walks 11 m South, then 6 m West. B walks 18 m East, then 18 m West. What is the distance between them?
Step-by-step:
1. A's final position: (-6, -11)
2. B's final position: (0, 0)
3. Distance = √[(-6-0)² + (-11-0)²] = √[-6² + -11²] = 13 m
two-persons, relative, distance

Question 10

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 11

A runner runs at 9 m/s on a circular track of length 641 m for 137 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 137 seconds = 9 × 137 = 1233 m
2. Number of laps = Distance / Track length = 1233 / 641 = 1.9 laps
circular, track, meeting, laps

Question 12

A person travels 12 m West, then 16 m South. Find the shortest distance from the starting point.
Step-by-step:
1. West and South are perpendicular directions
2. Shortest distance = √(12² + 16²) = √400 = 20 m
shortest-path, pythagoras

Question 13

A boat travels at 15 km/h in still water. The stream flows at 4 km/h. How long will it take to go 57 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 15 - 4 = 11 km/h
2. Time = Distance / Speed = 57 / 11 = 5.2 hours
boat, stream, upstream, downstream

Question 14

A train moves at 76 km/h for 45 minutes. What distance does it cover?
Time = 45 minutes = 0.75 hours
Distance = 76 × 0.75 = 57.0 km
speed, time, basic

Question 15

A train 345 m long is running at 83 km/h. How long will it take to cross a 216 m long platform?
Step-by-step:
1. Speed = 83 km/h = 23.1 m/s
2. Total distance = Train length + Platform length = 345 + 216 = 561 m
3. Time = Distance / Speed = 561 / 23.1 = 24.3 seconds
train, platform, pole, ssc

Question 16

A runner runs at 5 m/s on a circular track of length 469 m for 171 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 171 seconds = 5 × 171 = 855 m
2. Number of laps = Distance / Track length = 855 / 469 = 1.8 laps
circular, track, meeting, laps

Question 17

From point P, a person walks 12 m South, then 16 m West. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(12² + 16²)
3. = √(144 + 256) = √400 = 20 m
pythagoras, right-angle, shortest-distance

Question 18

A runner runs at 9 m/s on a circular track of length 731 m for 105 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 105 seconds = 9 × 105 = 945 m
2. Number of laps = Distance / Track length = 945 / 731 = 1.3 laps
circular, track, meeting, laps

Question 19

From point P, a person walks 20 m South, then 21 m West. 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 20

From point X, a person goes 15 m East, then 20 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(15² + 20²) = √625 = 25 m
shortest-path, pythagoras
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