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Distance Logic - Intermediate Level: grid distances INTERMEDIATE

Level up your distance logic skills with this comprehensive review. 20 intermediate-level problems await in Worksheet 14 of 30. Focus area: grid distances. Learn path length, position finding, coordinate geometry through systematic practice. Designed for mid-level learners seeking moderate complexity with mixed patterns.

📝 Worksheet 14 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 14 of 30 (46% complete)

Question 1

Train A at 63 km/h and Train B at 60 km/h start from stations 387 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 = 63 + 60 = 123 km/h
2. Time = Distance / Relative Speed = 387 / 123 = 3.1 hours
relative, meeting, catch-up

Question 2

A car travels at 75 km/h for 6 hours. What distance does it cover?
Distance = Speed × Time = 75 × 6 = 450 km
speed, time, basic

Question 3

A person starts from point O and walks 17m North, then 6m South. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 17m North, then 6m South
2. Net position: (0, 11)
3. Distance = √(0² + 11²) = √121 = 11 m
basic, movement, straight-line

Question 4

Two runners start from the same point on a circular track of length 588 m. Their speeds are 8 m/s and 10 m/s. If they run in opposite directions, when will they meet?
Step-by-step:
1. Relative speed (opposite direction) = 8 + 10 = 18 m/s
2. Time to meet = Track length / Relative speed = 588 / 18 = 32.7 seconds
circular, track, meeting, laps

Question 5

A boat travels at 15 km/h in still water. Stream speed is 3 km/h. What is the difference between upstream and downstream time for 40 km?
Step-by-step:
1. Downstream speed = 18 km/h, Time = 2.2 hours
2. Upstream speed = 12 km/h, Time = 3.3 hours
3. Difference = 3.3 - 2.2 = 1.1 hours
boat, stream, upstream, downstream

Question 6

A car travels at 63 km/h for 5 hours. What distance does it cover?
Distance = Speed × Time = 63 × 5 = 315 km
speed, time, basic

Question 7

A train 222 m long is running at 60 km/h. How long will it take to cross a 227 m long platform?
Step-by-step:
1. Speed = 60 km/h = 16.7 m/s
2. Total distance = Train length + Platform length = 222 + 227 = 449 m
3. Time = Distance / Speed = 449 / 16.7 = 26.9 seconds
train, platform, pole, ssc

Question 8

A runner runs at 11 m/s on a circular track of length 578 m for 110 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 110 seconds = 11 × 110 = 1210 m
2. Number of laps = Distance / Track length = 1210 / 578 = 2.1 laps
circular, track, meeting, laps

Question 9

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
pythagoras, right-angle, shortest-distance

Question 10

Car A at 62 km/h and Car B at 69 km/h start from the same point in the same direction. How long will it take for them to be 508 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |69 - 62| = 7 km/h
2. Time = Distance / Relative Speed = 508 / 7 = 72.6 hours
3. The second car will be 508 km ahead after 72.6 hours
relative, meeting, catch-up

Question 11

A train 276 m long is running at 68 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 68 km/h = 18.9 m/s
2. Time = Length / Speed = 276 / 18.9 = 14.6 seconds
train, platform, pole, ssc

Question 12

A person walks 11 m East, then 14 m East, then 17 m East, then 13 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 13 m North
- East-West: 42 m East
2. Displacement = √(42² + 13²) = √1933 = 44 m
3. Total distance walked = 55 m
multi-stage, displacement, complex

Question 13

Two runners start from the same point on a circular track of length 695 m. Their speeds are 9 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 - 9| = 3 m/s
2. Time to meet = Track length / Relative speed = 695 / 3 = 231.7 seconds
circular, track, meeting, laps

Question 14

A train moves at 39 km/h for 15 minutes. What distance does it cover?
Time = 15 minutes = 0.25 hours
Distance = 39 × 0.25 = 9.8 km
speed, time, basic

Question 15

Two persons A and B start from the same point. A walks 7 m East, then 13 m East. B walks 16 m North, then 20 m North, then 19 m East. What is the distance between them?
Step-by-step:
1. A's final position: (20, 0)
2. B's final position: (19, 36)
3. Distance = √[(20-19)² + (0-36)²] = √[1² + -36²] = 36 m
two-persons, relative, distance

Question 16

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

Question 17

A person walks 19 m East, then 15 m East, then 25 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 25 m North
- East-West: 34 m East
2. Displacement = √(34² + 25²) = √1781 = 42 m
3. Total distance walked = 59 m
multi-stage, displacement, complex

Question 18

A train 262 m long is running at 78 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 78 km/h = 21.7 m/s
2. Time = Length / Speed = 262 / 21.7 = 12.1 seconds
train, platform, pole, ssc

Question 19

A 152 cm tall person casts a 300 cm shadow. A building casts a 515 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 300/152 = 1.97
2. For object: Shadow / Height = 1.97
3. Height = Shadow / Ratio = 515 / 1.97 = 260.9 cm
shadow, similar-triangles, ssc

Question 20

A person walks 11 m North, then 17 m North, then 12 m East. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 28 m North
- East-West: 12 m East
2. Displacement = √(12² + 28²) = √928 = 30 m
3. Total distance walked = 40 m
multi-stage, displacement, complex
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