Question 1
A car travels at 41 km/h for 5 hours. What distance does it cover?
Distance = Speed × Time = 41 × 5 = 205 km
Distance Logic - Intermediate Level: displacement problems INTERMEDIATE
Comprehensive weakness targeting worksheet covering 20 intermediate-level distance logic problems. Worksheet 18 of 30 emphasizes displacement problems. Master route mapping, distance measurement, relative distances through detailed explanations. Difficulty: moderate complexity with mixed patterns. Tailored for mid-level preparation.
What you'll learn in this worksheet:
- Achieve proficiency in route mapping by completing this worksheet
- Develop strong distance measurement skills with practical problems
- Improve your distance logic solving speed through weakness targeting
- Gain confidence in identifying relative distances patterns
- Master real-world applications of displacement problems
Your progress through Distance Logic
Worksheet 18 of 30 (60% complete)
Question 2
A person starts from point O and walks 23m South, then 24m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 23m South, then 24m East
2. Net position: (24, -23)
3. Distance = √(24² + -23²) = √1105 = 33 m
1. Track movements: 23m South, then 24m East
2. Net position: (24, -23)
3. Distance = √(24² + -23²) = √1105 = 33 m
Question 3
A train moves at 80 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 80 × 0.25 = 20.0 km
Distance = 80 × 0.25 = 20.0 km
Question 4
Two persons A and B start from the same point. A walks 10 m West, then 5 m North, then 9 m North. B walks 16 m East, then 16 m South. What is the distance between them?
Step-by-step:
1. A's final position: (-10, 14)
2. B's final position: (16, -16)
3. Distance = √[(-10-16)² + (14--16)²] = √[-26² + 30²] = 40 m
1. A's final position: (-10, 14)
2. B's final position: (16, -16)
3. Distance = √[(-10-16)² + (14--16)²] = √[-26² + 30²] = 40 m
Question 5
A boat travels at 18 km/h in still water. The stream flows at 5 km/h. How long will it take to go 49 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 18 - 5 = 13 km/h
2. Time = Distance / Speed = 49 / 13 = 3.8 hours
1. Upstream speed = Boat speed - Stream speed = 18 - 5 = 13 km/h
2. Time = Distance / Speed = 49 / 13 = 3.8 hours
Question 6
A train 296 m long is running at 89 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 89 km/h = 24.7 m/s
2. Time = Length / Speed = 296 / 24.7 = 12.0 seconds
1. Speed = 89 km/h = 24.7 m/s
2. Time = Length / Speed = 296 / 24.7 = 12.0 seconds
Question 7
A train 380 m long is running at 50 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 50 km/h = 13.9 m/s
2. Time = Length / Speed = 380 / 13.9 = 27.4 seconds
1. Speed = 50 km/h = 13.9 m/s
2. Time = Length / Speed = 380 / 13.9 = 27.4 seconds
Question 8
A person travels from A to B at 42 km/h and returns at 64 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 × 42 × 64) / (42 + 64)
3. = 5376 / 106 = 50.7 km/h
1. For equal distances, Average Speed = (2 × v1 × v2) / (v1 + v2)
2. = (2 × 42 × 64) / (42 + 64)
3. = 5376 / 106 = 50.7 km/h
Question 9
A 158 cm tall person casts a 230 cm shadow. A building casts a 325 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 230/158 = 1.46
2. For object: Shadow / Height = 1.46
3. Height = Shadow / Ratio = 325 / 1.46 = 223.3 cm
1. Ratio of shadow to height = 230/158 = 1.46
2. For object: Shadow / Height = 1.46
3. Height = Shadow / Ratio = 325 / 1.46 = 223.3 cm
Question 10
From point P, a person walks 12 m North, then 16 m East. 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
1. These movements form a right angle
2. Shortest distance = √(12² + 16²)
3. = √(144 + 256) = √400 = 20 m
Question 11
A person travels from A to B at 37 km/h and returns at 49 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 × 37 × 49) / (37 + 49)
3. = 3626 / 86 = 42.2 km/h
1. For equal distances, Average Speed = (2 × v1 × v2) / (v1 + v2)
2. = (2 × 37 × 49) / (37 + 49)
3. = 3626 / 86 = 42.2 km/h
Question 12
A train 262 m long is running at 79 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 79 km/h = 21.9 m/s
2. Time = Length / Speed = 262 / 21.9 = 11.9 seconds
1. Speed = 79 km/h = 21.9 m/s
2. Time = Length / Speed = 262 / 21.9 = 11.9 seconds
Question 13
A train moves at 46 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 46 × 0.5 = 23.0 km
Distance = 46 × 0.5 = 23.0 km
Question 14
A 174 cm tall person casts a 184 cm shadow. A nearby building is 908 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 174/184 = 0.95
2. For object: Height / Shadow = 0.95
3. Shadow = Height / Ratio = 908 / 0.95 = 960.2 cm
1. Ratio of height to shadow length = 174/184 = 0.95
2. For object: Height / Shadow = 0.95
3. Shadow = Height / Ratio = 908 / 0.95 = 960.2 cm
Question 15
A person starts from point O and walks 19m North, then 20m South, then 8m South. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 19m North, then 20m South, then 8m South
2. Net position: (0, -9)
3. Distance = √(0² + -9²) = √81 = 9 m
1. Track movements: 19m North, then 20m South, then 8m South
2. Net position: (0, -9)
3. Distance = √(0² + -9²) = √81 = 9 m
Question 16
A boat travels at 14 km/h in still water. Stream speed is 5 km/h. What is the difference between upstream and downstream time for 53 km?
Step-by-step:
1. Downstream speed = 19 km/h, Time = 2.8 hours
2. Upstream speed = 9 km/h, Time = 5.9 hours
3. Difference = 5.9 - 2.8 = 3.1 hours
1. Downstream speed = 19 km/h, Time = 2.8 hours
2. Upstream speed = 9 km/h, Time = 5.9 hours
3. Difference = 5.9 - 2.8 = 3.1 hours
Question 17
From point P, a person walks 7 m West, then 24 m South. 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
1. These movements form a right angle
2. Shortest distance = √(7² + 24²)
3. = √(49 + 576) = √625 = 25 m
Question 18
A train moves at 76 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 76 × 0.25 = 19.0 km
Distance = 76 × 0.25 = 19.0 km
Question 19
A 179 cm tall person casts a 180 cm shadow. A building casts a 530 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 180/179 = 1.01
2. For object: Shadow / Height = 1.01
3. Height = Shadow / Ratio = 530 / 1.01 = 527.1 cm
1. Ratio of shadow to height = 180/179 = 1.01
2. For object: Shadow / Height = 1.01
3. Height = Shadow / Ratio = 530 / 1.01 = 527.1 cm
Question 20
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
1. These movements form a right angle
2. Shortest distance = √(20² + 21²)
3. = √(400 + 441) = √841 = 29 m
💪 Progress update: 58% complete. Worksheet 18 awaits!