Lesson 57 of 100 | Quantitative Aptitude / Speed, Distance and Time / चाल, दूरी और समय
Speed, distance, time and unit conversions
Learning outcome
Relate speed, distance and time, convert their units correctly, and separate moving time from the elapsed time of a journey.
Concepts and assumptions
Speed describes distance travelled per unit of time. A constant speed of 36 km/h means covering 36 km in each hour of motion. For constant speed:
Distance = speed × time.
Speed = distance ÷ time; time = distance ÷ speed.
These relationships follow from equal distances in equal time intervals. Dividing the accumulated distance by the number of intervals recovers the distance per interval.
Use a positive time when calculating speed and a positive speed when calculating travel time. At zero speed, no positive distance is covered. Assume steady motion on each stated moving part, with acceleration ignored. Include only the stops explicitly stated.
Units must match. Kilometres with hours give km/h; metres with seconds give m/s. Since 1 km = 1000 m and 1 h = 3600 s:
1 km/h = 1000/3600 m/s = 5/18 m/s.
Convert km/h to m/s by multiplying by 5/18; reverse the conversion by multiplying by 18/5. Also, 1 h = 60 min and 1 min = 60 s.
Hours and minutes are not decimal digits: 1 h 30 min = 1.5 h, not 1.30 h. Convert the minutes before substituting.
Distance measures the route actually travelled, not the straight-line separation of the endpoints. When calculating moving speed, remove stopping time. When a question asks about the whole journey, its elapsed time includes stops; these are different quantities.
Worked examples
Example 1 — Distance from minutes. A cyclist maintains 36 km/h for 45 minutes. Time = 45/60 = 3/4 h. Distance = 36 × 3/4 = 27 km. The smaller time unit must be converted before multiplying by an hourly speed.
Example 2 — Convert before dividing. A vehicle maintains 17.5 m/s over 126 km without stops. Speed = 17.5 × 18/5 = 63 km/h. Time = 126 ÷ 63 = 2 h. Check: 63 × 2 = 126 km.
Example 3 — Remove a stop. A van covers 143 km in 3 h from departure to arrival, including one 15-minute stop. It maintains the same speed whenever moving. Moving time = 3 - 15/60 = 11/4 h. Moving speed = 143 ÷ (11/4) = 52 km/h. Check: 52 × 11/4 = 143 km. This is not its whole-journey average speed.
Common mistakes
Do not divide kilometres by seconds and label the result km/h. Do not read 2.75 h as 2 h 75 min. Decide whether the requested time includes waiting before choosing the formula.
Practice questions
- A cyclist maintains 14 km/h for 1 h 45 min. How far does the cyclist travel?
- A runner covers 875 m in 2 min 5 s at constant speed. Find the speed in m/s and km/h.
- A bus covers 154 km at 56 km/h without stops. Find the time in hours and minutes.
- A car covers 39 km at a constant moving speed of 65 km/h and stops once for 9 minutes during the trip. Find its total elapsed journey time.
Worked answers
- Time = 1 + 45/60 = 7/4 h. Distance = 14 × 7/4 = 24.5 km.
- Time = 2 × 60 + 5 = 125 s. Speed = 875 ÷ 125 = 7 m/s. In km/h, 7 × 18/5 = 25.2 km/h.
- Time = 154 ÷ 56 = 2.75 h. The fractional hour is 0.75 × 60 = 45 minutes, so the journey takes 2 h 45 min.
- Moving time = 39 ÷ 65 = 0.6 h = 36 minutes. Add the stop: elapsed time = 36 + 9 = 45 minutes.