Time, Speed & Distance – Solved Problems

Time, Speed and Distance problems are fundamental in arithmetic and appear frequently in school exams and competitive tests. These problems are based on the simple relationship between time, speed, and distance.

Key Formulas:

Speed = Distance ÷ Time
Time = Distance ÷ Speed
Distance = Speed × Time
Average Speed = Total Distance ÷ Total Time
Relative Speed (same direction) = |v₁ − v₂|
Relative Speed (opposite direction) = v₁ + v₂

Problem 1: Basic speed calculation

A car travels 180 km in 3 hours. Find its speed.

Solution:
Speed = Distance ÷ Time
= 180 ÷ 3
Speed = 60 km/h

Problem 2: Find time taken

A cyclist travels at a speed of 15 km/h. How long will he take to cover 90 km?

Solution:
Time = Distance ÷ Speed
= 90 ÷ 15
Time = 6 hours

Problem 3: Average speed

A man travels 60 km at 30 km/h and returns at 20 km/h. Find his average speed.

Solution:
Time going = 60 ÷ 30 = 2 hours
Time returning = 60 ÷ 20 = 3 hours
Total distance = 120 km
Total time = 5 hours
Average speed = 120 ÷ 5 = 24 km/h

Problem 4: Relative speed (same direction)

Two cars move in the same direction at speeds of 60 km/h and 45 km/h. Find their relative speed.

Solution:
Relative speed = |60 − 45| = 15 km/h

Problem 5: Relative speed (opposite direction)

Two trains are moving towards each other at speeds of 40 km/h and 60 km/h. Find their relative speed.

Solution:
Relative speed = 40 + 60 = 100 km/h

Problem 6: Train crossing a platform

A train 120 m long crosses a platform 180 m long in 15 seconds. Find the speed of the train.

Solution:
Total distance = 120 + 180 = 300 m
Speed = 300 ÷ 15 = 20 m/s
Convert to km/h = 20 × 18/5 = 72 km/h

Problem 7: Boat and stream

A boat goes downstream at 18 km/h and upstream at 12 km/h. Find the speed of the boat in still water.

Solution:
Speed in still water = (18 + 12) ÷ 2 = 15 km/h

Problem 8: Distance comparison word problem

A person walks at 5 km/h for 2 hours and then runs at 10 km/h for 1 hour. Find the total distance covered.

Solution:
Walking distance = 5 × 2 = 10 km
Running distance = 10 × 1 = 10 km
Total distance = 20 km

Exam Tips

Always convert units before solving (m/s ↔ km/h)
For average speed, never average speeds directly unless distances are equal
Train problems require total distance calculation
Boat problems involve still water and stream speeds

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SOLVED PROBLEMS: TIME, SPEED & DISTANCE