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Distance Logic - Intermediate-Advanced Level: route mapping INTERMEDIATE-ADVANCED

Strategic expert challenge ★ for distance logic: 20 intermediate-advanced-level problems. Worksheet 19 of 30 - Focus: route mapping. Develop expertise in distance measurement, relative distances, path length with step-by-step solutions. Ideal for advanced developing learners targeting advanced concepts with increasing complexity.

📝 Worksheet 19 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 19 of 30 (63% complete)

Question 1

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

Question 2

A car travels at 32 km/h for 4 hours. What distance does it cover?
Distance = Speed × Time = 32 × 4 = 128 km
speed, time, basic

Question 3

A train moves at 57 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 57 × 0.5 = 28.5 km
speed, time, basic

Question 4

A boat travels at 23 km/h in still water. The stream flows at 8 km/h. How long will it take to go 69 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 23 - 8 = 15 km/h
2. Time = Distance / Speed = 69 / 15 = 4.6 hours
boat, stream, upstream, downstream

Question 5

A person walks from a point where his shadow length is measured to another point. The distances from a lamp post are 49 m and 97 m respectively. How far did he walk?
Step-by-step:
1. First position: distance from pole = 49 m
2. Second position: distance from pole = 97 m
3. Distance between positions = 97 - 49 = 48 m
shadow, similar-triangles, ssc

Question 6

From point P, a person walks 20 m West, then 21 m South. 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 7

From point X, a person goes 5 m East, then 12 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(5² + 12²) = √169 = 13 m
shortest-path, pythagoras

Question 8

A boat travels 65 km downstream in 2.2 hours and upstream in 5.0 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: 65/(x + 8) = 2.2
3. Upstream: 65/(x - 8) = 5.0
4. Solving gives x = 21 km/h
boat, stream, upstream, downstream

Question 9

Two persons A and B start from the same point. A walks 20 m West, then 18 m East. B walks 10 m West, then 13 m West, then 14 m South. What is the distance between them?
Step-by-step:
1. A's final position: (-2, 0)
2. B's final position: (-23, -14)
3. Distance = √[(-2--23)² + (0--14)²] = √[21² + 14²] = 25 m
two-persons, relative, distance

Question 10

A person walks 11 m North, then 23 m East, then 21 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 32 m North
- East-West: 23 m East
2. Displacement = √(23² + 32²) = √1553 = 39 m
3. Total distance walked = 55 m
multi-stage, displacement, complex

Question 11

A person travels from A to B at 41 km/h and returns at 68 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 × 41 × 68) / (41 + 68)
3. = 5576 / 109 = 51.2 km/h
average, speed, distance

Question 12

From point P, a person walks 5 m North, then 12 m East. 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 13

Two persons A and B start from the same point. A walks 15 m West, then 17 m North, then 13 m South. B walks 13 m North, then 14 m North, then 9 m North. What is the distance between them?
Step-by-step:
1. A's final position: (-15, 4)
2. B's final position: (0, 36)
3. Distance = √[(-15-0)² + (4-36)²] = √[-15² + -32²] = 35 m
two-persons, relative, distance

Question 14

A train moves at 79 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 79 × 0.25 = 19.8 km
speed, time, basic

Question 15

Two persons A and B start from the same point. A walks 8 m East, then 17 m East, then 8 m East. B walks 11 m North, then 9 m South, then 18 m North. What is the distance between them?
Step-by-step:
1. A's final position: (33, 0)
2. B's final position: (0, 20)
3. Distance = √[(33-0)² + (0-20)²] = √[33² + -20²] = 39 m
two-persons, relative, distance

Question 16

A person walks 3 m North, then 4 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(3² + 4²) = √25 = 5 m
shortest-path, pythagoras

Question 17

Car A at 53 km/h and Car B at 71 km/h start from the same point in the same direction. How long will it take for them to be 536 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |71 - 53| = 18 km/h
2. Time = Distance / Relative Speed = 536 / 18 = 29.8 hours
3. The second car will be 536 km ahead after 29.8 hours
relative, meeting, catch-up

Question 18

A person starts from point O and walks 23m West, then 5m South, then 9m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 23m West, then 5m South, then 9m East
2. Net position: (-14, -5)
3. Distance = √(-14² + -5²) = √221 = 15 m
basic, movement, straight-line

Question 19

Two persons A and B start from the same point. A walks 12 m West, then 11 m East. B walks 20 m North, then 11 m East. What is the distance between them?
Step-by-step:
1. A's final position: (-1, 0)
2. B's final position: (11, 20)
3. Distance = √[(-1-11)² + (0-20)²] = √[-12² + -20²] = 23 m
two-persons, relative, distance

Question 20

A person travels at 39 km/h for 2 hours and then at 74 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (39 + 74) / 2 = 56.5 km/h
average, speed, distance
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