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Distance Logic - Beginner Level: shortest path BEGINNER

Ready to master distance logic? This concept mastery features 20 beginner-level challenges. Worksheet 2 of 30 sharpens your shortest path skills. Master shortest path, displacement problems, route mapping through guided practice. Perfect for entry-level test preparation.

📝 Worksheet 2 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 2 of 30 (6% complete)

Question 1

A person starts from point O and walks 7m North, then 14m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 7m North, then 14m West
2. Net position: (-14, 7)
3. Distance = √(-14² + 7²) = √245 = 16 m
basic, movement, straight-line

Question 2

A person travels at 35 km/h for 2 hours and then at 40 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (35 + 40) / 2 = 37.5 km/h
average, speed, distance

Question 3

A train moves at 57 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 57 × 0.25 = 14.2 km
speed, time, basic

Question 4

Car A at 63 km/h and Car B at 74 km/h start from the same point in the same direction. How long will it take for them to be 587 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |74 - 63| = 11 km/h
2. Time = Distance / Relative Speed = 587 / 11 = 53.4 hours
3. The second car will be 587 km ahead after 53.4 hours
relative, meeting, catch-up

Question 5

A boat travels 71 km downstream in 3.2 hours and upstream in 7.1 hours. The stream speed is 6 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 6 km/h
2. Downstream: 71/(x + 6) = 3.2
3. Upstream: 71/(x - 6) = 7.1
4. Solving gives x = 16 km/h
boat, stream, upstream, downstream

Question 6

Two runners start from the same point on a circular track of length 722 m. Their speeds are 6 m/s and 9 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |9 - 6| = 3 m/s
2. Time to meet = Track length / Relative speed = 722 / 3 = 240.7 seconds
circular, track, meeting, laps

Question 7

Two persons A and B start from the same point. A walks 15 m South, then 7 m East, then 7 m South. B walks 5 m South, then 18 m West, then 15 m North. What is the distance between them?
Step-by-step:
1. A's final position: (7, -22)
2. B's final position: (-18, 10)
3. Distance = √[(7--18)² + (-22-10)²] = √[25² + -32²] = 41 m
two-persons, relative, distance

Question 8

A person travels at 30 km/h for 2 hours and then at 63 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (30 + 63) / 2 = 46.5 km/h
average, speed, distance

Question 9

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 10

Two persons A and B start from the same point. A walks 15 m West, then 9 m North, then 14 m North. B walks 8 m West, then 18 m North, then 10 m East. What is the distance between them?
Step-by-step:
1. A's final position: (-15, 23)
2. B's final position: (2, 18)
3. Distance = √[(-15-2)² + (23-18)²] = √[-17² + 5²] = 18 m
two-persons, relative, distance

Question 11

A person starts from point O and walks 6m West, then 24m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 6m West, then 24m West
2. Net position: (-30, 0)
3. Distance = √(-30² + 0²) = √900 = 30 m
basic, movement, straight-line

Question 12

From point P, a person walks 20 m East, then 21 m North. 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 13

A runner runs at 8 m/s on a circular track of length 611 m for 162 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 162 seconds = 8 × 162 = 1296 m
2. Number of laps = Distance / Track length = 1296 / 611 = 2.1 laps
circular, track, meeting, laps

Question 14

From point X, a person goes 8 m East, then 6 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(8² + 6²) = √100 = 10 m
shortest-path, pythagoras

Question 15

Two runners start from the same point on a circular track of length 641 m. Their speeds are 9 m/s and 12 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 9 + 12 = 21 m/s
2. Time to meet = Track length / Relative speed = 641 / 21 = 30.5 seconds
circular, track, meeting, laps

Question 16

Car A at 67 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 356 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |66 - 67| = 1 km/h
2. Time = Distance / Relative Speed = 356 / 1 = 356.0 hours
3. The first car will be 356 km ahead after 356.0 hours
relative, meeting, catch-up

Question 17

A person starts from point O and walks 23m East, then 17m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 23m East, then 17m West
2. Net position: (6, 0)
3. Distance = √(6² + 0²) = √36 = 6 m
basic, movement, straight-line

Question 18

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 19

A person starts from point O and walks 8m South, then 13m West, then 25m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 8m South, then 13m West, then 25m East
2. Net position: (12, -8)
3. Distance = √(12² + -8²) = √208 = 14 m
basic, movement, straight-line

Question 20

A boat travels at 14 km/h in still water. The stream flows at 5 km/h. How long will it take to go 77 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 14 - 5 = 9 km/h
2. Time = Distance / Speed = 77 / 9 = 8.6 hours
boat, stream, upstream, downstream
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