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Distance Logic - Beginner-Intermediate Level: distance-time relationships BEGINNER-INTERMEDIATE

Intensive quick response training 🎯 drill: 20 beginner-intermediate-level distance logic questions. Worksheet 10 of 30 hones your distance-time relationships abilities. Practice displacement problems, route mapping, distance measurement under timed conditions. Best for developing students seeking building on fundamentals with moderate challenges.

📝 Worksheet 10 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 10 of 30 (33% complete)

Question 1

A person travels 12 m West, then 16 m South. Find the shortest distance from the starting point.
Step-by-step:
1. West and South are perpendicular directions
2. Shortest distance = √(12² + 16²) = √400 = 20 m
shortest-path, pythagoras

Question 2

A boat travels 62 km downstream in 2.4 hours and upstream in 3.9 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: 62/(x + 5) = 2.4
3. Upstream: 62/(x - 5) = 3.9
4. Solving gives x = 21 km/h
boat, stream, upstream, downstream

Question 3

A person travels at 60 km/h for 2 hours and then at 58 km/h for 2 hours. What is the average speed?
Step-by-step:
1. For equal time intervals, Average Speed = (v1 + v2) / 2
2. = (60 + 58) / 2 = 59.0 km/h
average, speed, distance

Question 4

A person starts from point O and walks 9m West, then 5m West. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 9m West, then 5m West
2. Net position: (-14, 0)
3. Distance = √(-14² + 0²) = √196 = 14 m
basic, movement, straight-line

Question 5

A person travels from A to B at 43 km/h and returns at 55 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 × 55) / (43 + 55)
3. = 4730 / 98 = 48.3 km/h
average, speed, distance

Question 6

A person walks 19 m West, then 23 m North, then 21 m West, then 18 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 23 m North
- East-West: -58 m West
2. Displacement = √(-58² + 23²) = √3893 = 62 m
3. Total distance walked = 81 m
multi-stage, displacement, complex

Question 7

A boat travels at 19 km/h in still water. Stream speed is 6 km/h. What is the difference between upstream and downstream time for 44 km?
Step-by-step:
1. Downstream speed = 25 km/h, Time = 1.8 hours
2. Upstream speed = 13 km/h, Time = 3.4 hours
3. Difference = 3.4 - 1.8 = 1.6 hours
boat, stream, upstream, downstream

Question 8

A person walks 9 m West, then 22 m East, then 11 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 0 m 0
- East-West: 2 m East
2. Displacement = √(2² + 0²) = √4 = 2 m
3. Total distance walked = 42 m
multi-stage, displacement, complex

Question 9

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 10

Car A at 69 km/h and Car B at 77 km/h start from the same point in the same direction. How long will it take for them to be 397 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |77 - 69| = 8 km/h
2. Time = Distance / Relative Speed = 397 / 8 = 49.6 hours
3. The second car will be 397 km ahead after 49.6 hours
relative, meeting, catch-up

Question 11

A person starts from point O and walks 20m South, then 10m North, then 15m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 20m South, then 10m North, then 15m North
2. Net position: (0, 5)
3. Distance = √(0² + 5²) = √25 = 5 m
basic, movement, straight-line

Question 12

A runner runs at 6 m/s on a circular track of length 775 m for 74 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 74 seconds = 6 × 74 = 444 m
2. Number of laps = Distance / Track length = 444 / 775 = 0.6 laps
circular, track, meeting, laps

Question 13

A person starts from point O and walks 21m North, then 15m South. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 21m North, then 15m South
2. Net position: (0, 6)
3. Distance = √(0² + 6²) = √36 = 6 m
basic, movement, straight-line

Question 14

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 15

A person travels from A to B at 35 km/h and returns at 54 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 × 35 × 54) / (35 + 54)
3. = 3780 / 89 = 42.5 km/h
average, speed, distance

Question 16

A 180 cm tall person casts a 136 cm shadow. A building casts a 580 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 136/180 = 0.76
2. For object: Shadow / Height = 0.76
3. Height = Shadow / Ratio = 580 / 0.76 = 767.6 cm
shadow, similar-triangles, ssc

Question 17

A train 289 m long is running at 88 km/h. How long will it take to cross a 264 m long platform?
Step-by-step:
1. Speed = 88 km/h = 24.4 m/s
2. Total distance = Train length + Platform length = 289 + 264 = 553 m
3. Time = Distance / Speed = 553 / 24.4 = 22.6 seconds
train, platform, pole, ssc

Question 18

Two runners start from the same point on a circular track of length 684 m. Their speeds are 11 m/s and 12 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |12 - 11| = 1 m/s
2. Time to meet = Track length / Relative speed = 684 / 1 = 684.0 seconds
circular, track, meeting, laps

Question 19

A person travels at 38 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. = (38 + 40) / 2 = 39.0 km/h
average, speed, distance

Question 20

Car A at 57 km/h and Car B at 61 km/h start from the same point in the same direction. How long will it take for them to be 580 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |61 - 57| = 4 km/h
2. Time = Distance / Relative Speed = 580 / 4 = 145.0 hours
3. The second car will be 580 km ahead after 145.0 hours
relative, meeting, catch-up
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