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Distance Logic - Beginner-Intermediate Level: coordinate geometry BEGINNER-INTERMEDIATE

Strategic fast track practice for distance logic: 20 beginner-intermediate-level problems. Worksheet 9 of 30 - Focus: coordinate geometry. Develop expertise in shortest path, displacement problems, route mapping with step-by-step solutions. Ideal for developing learners targeting building on fundamentals with moderate challenges.

📝 Worksheet 9 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 9 of 30 (30% complete)

Question 1

Two persons A and B start from the same point. A walks 14 m South, then 11 m West. B walks 11 m East, then 18 m West, then 19 m South. What is the distance between them?
Step-by-step:
1. A's final position: (-11, -14)
2. B's final position: (-7, -19)
3. Distance = √[(-11--7)² + (-14--19)²] = √[-4² + 5²] = 6 m
two-persons, relative, distance

Question 2

A car travels at 67 km/h for 6 hours. What distance does it cover?
Distance = Speed × Time = 67 × 6 = 402 km
speed, time, basic

Question 3

A runner runs at 11 m/s on a circular track of length 523 m for 176 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 176 seconds = 11 × 176 = 1936 m
2. Number of laps = Distance / Track length = 1936 / 523 = 3.7 laps
circular, track, meeting, laps

Question 4

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 5

Train A at 64 km/h and Train B at 50 km/h start from stations 312 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 = 64 + 50 = 114 km/h
2. Time = Distance / Relative Speed = 312 / 114 = 2.7 hours
relative, meeting, catch-up

Question 6

A person starts from point O and walks 20m North, then 11m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 20m North, then 11m West
2. Net position: (-11, 20)
3. Distance = √(-11² + 20²) = √521 = 23 m
basic, movement, straight-line

Question 7

Two runners start from the same point on a circular track of length 410 m. Their speeds are 6 m/s and 15 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |15 - 6| = 9 m/s
2. Time to meet = Track length / Relative speed = 410 / 9 = 45.6 seconds
circular, track, meeting, laps

Question 8

A boat travels at 15 km/h in still water. The stream flows at 7 km/h. How long will it take to go 74 km downstream?
Step-by-step:
1. Downstream speed = Boat speed + Stream speed = 15 + 7 = 22 km/h
2. Time = Distance / Speed = 74 / 22 = 3.4 hours
boat, stream, upstream, downstream

Question 9

Train A at 44 km/h and Train B at 52 km/h start from stations 401 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 = 44 + 52 = 96 km/h
2. Time = Distance / Relative Speed = 401 / 96 = 4.2 hours
relative, meeting, catch-up

Question 10

A person starts from point O and walks 15m West, then 22m East, then 16m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 15m West, then 22m East, then 16m West
2. Net position: (-9, 0)
3. Distance = √(-9² + 0²) = √81 = 9 m
basic, movement, straight-line

Question 11

A person travels at 56 km/h for 2 hours and then at 68 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (56 + 68) / 2 = 62.0 km/h
average, speed, distance

Question 12

A car travels at 57 km/h for 4 hours. What distance does it cover?
Distance = Speed × Time = 57 × 4 = 228 km
speed, time, basic

Question 13

From point P, a person walks 3 m North, then 4 m East. 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 14

A person walks 22 m North, then 19 m East, then 25 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 47 m North
- East-West: 19 m East
2. Displacement = √(19² + 47²) = √2570 = 51 m
3. Total distance walked = 66 m
multi-stage, displacement, complex

Question 15

A train moves at 32 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 32 × 0.25 = 8.0 km
speed, time, basic

Question 16

A 160 cm tall person casts a 250 cm shadow. A building casts a 464 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 250/160 = 1.56
2. For object: Shadow / Height = 1.56
3. Height = Shadow / Ratio = 464 / 1.56 = 297.0 cm
shadow, similar-triangles, ssc

Question 17

A person travels at 47 km/h for 2 hours and then at 80 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (47 + 80) / 2 = 63.5 km/h
average, speed, distance

Question 18

A person starts from point O and walks 9m East, then 12m South, then 15m South. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 9m East, then 12m South, then 15m South
2. Net position: (9, -27)
3. Distance = √(9² + -27²) = √810 = 28 m
basic, movement, straight-line

Question 19

A boat travels at 17 km/h in still water. The stream flows at 8 km/h. How long will it take to go 77 km upstream?
Step-by-step:
1. Upstream speed = Boat speed - Stream speed = 17 - 8 = 9 km/h
2. Time = Distance / Speed = 77 / 9 = 8.6 hours
boat, stream, upstream, downstream

Question 20

A train moves at 38 km/h for 30 minutes. What distance does it cover?
Time = 30 minutes = 0.5 hours
Distance = 38 × 0.5 = 19.0 km
speed, time, basic
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