QR: Speed, Distance, Time & Rates
The Core Formula
Speed = Distance / Time → Distance = Speed × Time → Time = Distance / Speed
Common QR Rate Problems
Journey Problems
Example: A car travels 120km at 60km/h, then 80km at 40km/h. What is the average speed?
Common mistake: averaging the speeds (60+40)/2 = 50km/h. WRONG!
Correct method: Total distance = 200km. Total time = 120/60 + 80/40 = 2 + 2 = 4 hours. Average speed = 200/4 = 50km/h (happens to be 50 here, but the method matters).
Work Rate Problems
If Worker A can complete a job in 6 hours and Worker B in 4 hours, how long do they take together?
Rate A = 1/6 job per hour. Rate B = 1/4 job per hour. Combined rate = 1/6 + 1/4 = 5/12. Time = 12/5 = 2.4 hours.
Flow Rate Problems
A pipe fills a tank at 30 litres/minute. The tank holds 1500 litres. How long to fill? Time = 1500/30 = 50 minutes.
Cost Rate Problems
Electricity costs $0.28 per kWh. A 2000W heater runs for 5 hours. Cost = (2000/1000) × 5 × 0.28 = 2 × 5 × 0.28 = $2.80.
Unit Conversions for Rate Problems
- km/h to m/s: divide by 3.6 (or multiply by 5/18)
- m/s to km/h: multiply by 3.6 (or multiply by 18/5)
- minutes to hours: divide by 60
- hours to minutes: multiply by 60
Multi-Step Rate Problems
Many QR questions involve multiple steps. Break the problem down:
- Identify what you are asked to find
- Identify what information is given
- Determine the intermediate calculations needed
- Work step by step, keeping track of units