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Distance Logic - Advanced Level: distance-time relationships ADVANCED

Boost your speed and accuracy with this high difficulty set 📈 worksheet. Worksheet 25 of 30 presents 20 advanced-level distance logic problems. Focus on distance-time relationships while practicing route mapping, distance measurement, relative distances. Difficulty: complex scenarios and multi-step problems. Perfect for advanced test takers.

📝 Worksheet 25 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 25 of 30 (83% complete)

Question 1

A person walks 19 m West, then 21 m East, then 15 m South. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -15 m South
- East-West: 2 m East
2. Displacement = √(2² + -15²) = √229 = 15 m
3. Total distance walked = 55 m
multi-stage, displacement, complex

Question 2

A train 281 m long is running at 75 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 75 km/h = 20.8 m/s
2. Time = Length / Speed = 281 / 20.8 = 13.5 seconds
train, platform, pole, ssc

Question 3

A person walks 9 m South, then 20 m West, then 18 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -9 m South
- East-West: -38 m West
2. Displacement = √(-38² + -9²) = √1525 = 39 m
3. Total distance walked = 47 m
multi-stage, displacement, complex

Question 4

A runner runs at 5 m/s on a circular track of length 781 m for 97 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 97 seconds = 5 × 97 = 485 m
2. Number of laps = Distance / Track length = 485 / 781 = 0.6 laps
circular, track, meeting, laps

Question 5

A 151 cm tall person casts a 106 cm shadow. A building casts a 445 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 106/151 = 0.70
2. For object: Shadow / Height = 0.70
3. Height = Shadow / Ratio = 445 / 0.70 = 633.9 cm
shadow, similar-triangles, ssc

Question 6

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 7

A boat travels 69 km downstream in 3.0 hours and upstream in 5.3 hours. The stream speed is 5 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 5 km/h
2. Downstream: 69/(x + 5) = 3.0
3. Upstream: 69/(x - 5) = 5.3
4. Solving gives x = 18 km/h
boat, stream, upstream, downstream

Question 8

A person travels at 46 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. = (46 + 63) / 2 = 54.5 km/h
average, speed, distance

Question 9

Two persons A and B start from the same point. A walks 17 m East, then 8 m East. B walks 9 m North, then 13 m North. What is the distance between them?
Step-by-step:
1. A's final position: (25, 0)
2. B's final position: (0, 22)
3. Distance = √[(25-0)² + (0-22)²] = √[25² + -22²] = 33 m
two-persons, relative, distance

Question 10

A 164 cm tall person casts a 219 cm shadow. A nearby building is 902 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 164/219 = 0.75
2. For object: Height / Shadow = 0.75
3. Shadow = Height / Ratio = 902 / 0.75 = 1204.5 cm
shadow, similar-triangles, ssc

Question 11

Two runners start from the same point on a circular track of length 526 m. Their speeds are 9 m/s and 14 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 9 + 14 = 23 m/s
2. Time to meet = Track length / Relative speed = 526 / 23 = 22.9 seconds
circular, track, meeting, laps

Question 12

A boat travels 64 km downstream in 2.5 hours and upstream in 4.0 hours. The stream speed is 5 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 5 km/h
2. Downstream: 64/(x + 5) = 2.5
3. Upstream: 64/(x - 5) = 4.0
4. Solving gives x = 21 km/h
boat, stream, upstream, downstream

Question 13

Two runners start from the same point on a circular track of length 784 m. Their speeds are 9 m/s and 8 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |8 - 9| = 1 m/s
2. Time to meet = Track length / Relative speed = 784 / 1 = 784.0 seconds
circular, track, meeting, laps

Question 14

A person walks 5 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 = √(5² + 12²) = √169 = 13 m
shortest-path, pythagoras

Question 15

From point P, a person walks 9 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 = √(9² + 12²)
3. = √(81 + 144) = √225 = 15 m
pythagoras, right-angle, shortest-distance

Question 16

Train A at 55 km/h and Train B at 74 km/h start from stations 306 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 = 55 + 74 = 129 km/h
2. Time = Distance / Relative Speed = 306 / 129 = 2.4 hours
relative, meeting, catch-up

Question 17

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 18

Two persons A and B start from the same point. A walks 17 m West, then 15 m East. B walks 19 m East, then 14 m West, then 9 m East. What is the distance between them?
Step-by-step:
1. A's final position: (-2, 0)
2. B's final position: (14, 0)
3. Distance = √[(-2-14)² + (0-0)²] = √[-16² + 0²] = 16 m
two-persons, relative, distance

Question 19

Two runners start from the same point on a circular track of length 569 m. Their speeds are 10 m/s and 12 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 10 + 12 = 22 m/s
2. Time to meet = Track length / Relative speed = 569 / 22 = 25.9 seconds
circular, track, meeting, laps

Question 20

A boat travels at 13 km/h in still water. The stream flows at 3 km/h. How long will it take to go 70 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 13 - 3 = 10 km/h
2. Time = Distance / Speed = 70 / 10 = 7.0 hours
boat, stream, upstream, downstream
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