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Distance Logic - Advanced Level: Pythagorean theorem ADVANCED

Quick competitive exam prep session: 20 advanced-level distance logic questions. Worksheet 27 of 30 - Focus: Pythagorean theorem. Practice relative distances, path length, position finding with instant feedback. Great for advanced students needing complex scenarios and multi-step problems practice.

📝 Worksheet 27 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 27 of 30 (90% complete)

Question 1

A person travels from A to B at 43 km/h and returns at 53 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 × 43 × 53) / (43 + 53)
3. = 4558 / 96 = 47.5 km/h
average, speed, distance

Question 2

A person travels from A to B at 30 km/h and returns at 66 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 × 30 × 66) / (30 + 66)
3. = 3960 / 96 = 41.2 km/h
average, speed, distance

Question 3

Two persons A and B start from the same point. A walks 20 m North, then 7 m South, then 11 m South. B walks 16 m West, then 17 m North. What is the distance between them?
Step-by-step:
1. A's final position: (0, 2)
2. B's final position: (-16, 17)
3. Distance = √[(0--16)² + (2-17)²] = √[16² + -15²] = 22 m
two-persons, relative, distance

Question 4

A person walks 12 m North, then 16 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(12² + 16²) = √400 = 20 m
shortest-path, pythagoras

Question 5

A person travels at 40 km/h for 2 hours and then at 56 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (40 + 56) / 2 = 48.0 km/h
average, speed, distance

Question 6

A 157 cm tall person casts a 221 cm shadow. A nearby building is 713 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 157/221 = 0.71
2. For object: Height / Shadow = 0.71
3. Shadow = Height / Ratio = 713 / 0.71 = 1003.6 cm
shadow, similar-triangles, ssc

Question 7

A person walks 9 m North, then 12 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(9² + 12²) = √225 = 15 m
shortest-path, pythagoras

Question 8

A person travels at 55 km/h for 2 hours and then at 54 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (55 + 54) / 2 = 54.5 km/h
average, speed, distance

Question 9

A train moves at 62 km/h for 45 minutes. What distance does it cover?
Time = 45 minutes = 0.75 hours
Distance = 62 × 0.75 = 46.5 km
speed, time, basic

Question 10

From point P, a person walks 7 m South, then 24 m West. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(7² + 24²)
3. = √(49 + 576) = √625 = 25 m
pythagoras, right-angle, shortest-distance

Question 11

A person starts from point O and walks 13m North, then 14m South, then 7m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 13m North, then 14m South, then 7m East
2. Net position: (7, -1)
3. Distance = √(7² + -1²) = √50 = 7 m
basic, movement, straight-line

Question 12

A train 380 m long is running at 69 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 69 km/h = 19.2 m/s
2. Time = Length / Speed = 380 / 19.2 = 19.8 seconds
train, platform, pole, ssc

Question 13

A person travels at 30 km/h for 2 hours and then at 56 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 + 56) / 2 = 43.0 km/h
average, speed, distance

Question 14

A person travels from A to B at 43 km/h and returns at 61 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 × 43 × 61) / (43 + 61)
3. = 5246 / 104 = 50.4 km/h
average, speed, distance

Question 15

A train moves at 45 km/h for 45 minutes. What distance does it cover?
Time = 45 minutes = 0.75 hours
Distance = 45 × 0.75 = 33.8 km
speed, time, basic

Question 16

From point P, a person walks 12 m East, then 16 m North. 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 17

A train moves at 80 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 80 × 0.5 = 40.0 km
speed, time, basic

Question 18

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 19

A person walks 7 m North, then 24 m East. What is the straight-line distance from the starting point?
Step-by-step:
1. These are perpendicular movements
2. Straight-line distance = √(7² + 24²) = √625 = 25 m
shortest-path, pythagoras

Question 20

Two runners start from the same point on a circular track of length 489 m. Their speeds are 10 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 - 10| = 3 m/s
2. Time to meet = Track length / Relative speed = 489 / 3 = 163.0 seconds
circular, track, meeting, laps
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