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Distance Logic - Beginner-Intermediate Level: path length BEGINNER-INTERMEDIATE

Quick intensive drill ★ session: 20 beginner-intermediate-level distance logic questions. Worksheet 7 of 30 - Focus: path length. Practice path length, position finding, coordinate geometry with instant feedback. Great for developing students needing building on fundamentals with moderate challenges practice.

📝 Worksheet 7 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 7 of 30 (23% complete)

Question 1

A boat travels at 12 km/h in still water. Stream speed is 5 km/h. What is the difference between upstream and downstream time for 60 km?
Step-by-step:
1. Downstream speed = 17 km/h, Time = 3.5 hours
2. Upstream speed = 7 km/h, Time = 8.6 hours
3. Difference = 8.6 - 3.5 = 5.1 hours
boat, stream, upstream, downstream

Question 2

A train 151 m long is running at 78 km/h. How long will it take to cross a 138 m long platform?
Step-by-step:
1. Speed = 78 km/h = 21.7 m/s
2. Total distance = Train length + Platform length = 151 + 138 = 289 m
3. Time = Distance / Speed = 289 / 21.7 = 13.3 seconds
train, platform, pole, ssc

Question 3

A person starts from point O and walks 10m North, then 22m East, then 15m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 10m North, then 22m East, then 15m North
2. Net position: (22, 25)
3. Distance = √(22² + 25²) = √1109 = 33 m
basic, movement, straight-line

Question 4

A person starts from point O and walks 13m South, then 7m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 13m South, then 7m East
2. Net position: (7, -13)
3. Distance = √(7² + -13²) = √218 = 15 m
basic, movement, straight-line

Question 5

From point P, a person walks 3 m South, then 4 m West. 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 6

A person starts from point O and walks 25m East, then 16m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 25m East, then 16m East
2. Net position: (41, 0)
3. Distance = √(41² + 0²) = √1681 = 41 m
basic, movement, straight-line

Question 7

Train A at 69 km/h and Train B at 51 km/h start from stations 317 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 = 69 + 51 = 120 km/h
2. Time = Distance / Relative Speed = 317 / 120 = 2.6 hours
relative, meeting, catch-up

Question 8

A train 182 m long is running at 78 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 78 km/h = 21.7 m/s
2. Time = Length / Speed = 182 / 21.7 = 8.4 seconds
train, platform, pole, ssc

Question 9

A person starts from point O and walks 9m East, then 18m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 9m East, then 18m North
2. Net position: (9, 18)
3. Distance = √(9² + 18²) = √405 = 20 m
basic, movement, straight-line

Question 10

A train moves at 49 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 49 × 0.5 = 24.5 km
speed, time, basic

Question 11

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 12

Train A at 57 km/h and Train B at 59 km/h start from stations 583 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 = 57 + 59 = 116 km/h
2. Time = Distance / Relative Speed = 583 / 116 = 5.0 hours
relative, meeting, catch-up

Question 13

A person walks 24 m North, then 10 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(24² + 10²) = √676 = 26 m
shortest-path, pythagoras

Question 14

A boat travels 48 km downstream in 2.2 hours and upstream in 6.0 hours. The stream speed is 7 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 7 km/h
2. Downstream: 48/(x + 7) = 2.2
3. Upstream: 48/(x - 7) = 6.0
4. Solving gives x = 15 km/h
boat, stream, upstream, downstream

Question 15

A boat travels at 18 km/h in still water. The stream flows at 6 km/h. How long will it take to go 76 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 18 - 6 = 12 km/h
2. Time = Distance / Speed = 76 / 12 = 6.3 hours
boat, stream, upstream, downstream

Question 16

Car A at 53 km/h and Car B at 66 km/h start from the same point in the same direction. How long will it take for them to be 523 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |66 - 53| = 13 km/h
2. Time = Distance / Relative Speed = 523 / 13 = 40.2 hours
3. The second car will be 523 km ahead after 40.2 hours
relative, meeting, catch-up

Question 17

Two persons A and B start from the same point. A walks 17 m South, then 20 m East. B walks 17 m South, then 10 m West, then 11 m West. What is the distance between them?
Step-by-step:
1. A's final position: (20, -17)
2. B's final position: (-21, -17)
3. Distance = √[(20--21)² + (-17--17)²] = √[41² + 0²] = 41 m
two-persons, relative, distance

Question 18

Train A at 63 km/h and Train B at 69 km/h start from stations 561 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 = 63 + 69 = 132 km/h
2. Time = Distance / Relative Speed = 561 / 132 = 4.2 hours
relative, meeting, catch-up

Question 19

A person travels from A to B at 31 km/h and returns at 79 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 × 31 × 79) / (31 + 79)
3. = 4898 / 110 = 44.5 km/h
average, speed, distance

Question 20

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
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