Rates (harder)
Every question with a fully worked solution.
- Rates (harder) - Video - Converting Rates Watch
Theory
To convert a rate to new units, write the unit fact first, then change one unit at a time. \(12\) L/min is \(12 \times 60 = 720\) L/h. This Year 7 maths page shows how to change the time unit, the amount unit or both, and the shortcut between m/s and km/h.
Change the time unit. \(12\) L/min means \(12\) L every minute. An hour has \(60\) minutes, so multiply: \(12 \times 60 = 720\) L/h. A longer time gives a bigger amount; a shorter time gives a smaller amount, so divide.
Change the amount unit. Only the amount changes; the time stays the same: \(0.8\) m/h is \(0.8 \times 100 = 80\) cm/h.
Two units change? Change one unit, write the new rate, then change the other. Sometimes both change the same way: \(8\) km/L is \(8000\) m per \(1000\) mL, which is \(8\) m/mL.
Rounding. Round only at the end, to the places asked: \(1000\) kg/h \(= 1000 \div 3600 \approx 0.28\) kg/s (\(2\) decimal places).
m/s and km/h. Multiplying by \(3600\) and then dividing by \(1000\) is the same as multiplying by \(3.6\). So m/s \(\times 3.6 =\) km/h, and km/h \(\div 3.6 =\) m/s.
Hours and minutes. Change the minutes to hours: \(45\) min \(= \dfrac{45}{60}\) h \(= 0.75\) h, so \(1\) h \(45\) min \(= 1.75\) h.
Unit facts:
| Time | Length, volume, mass |
|---|---|
| \(1\) min \(= 60\) s | \(1\) km \(= 1000\) m |
| \(1\) h \(= 60\) min \(= 3600\) s | \(1\) m \(= 100\) cm |
| \(1\) day \(= 24\) h | \(1\) L \(= 1000\) mL |
| \(1\) kg \(= 1000\) g |
How to convert a rate
- Write the unit fact for the unit you are changing.
- Decide: should the number get bigger or smaller? Multiply or divide.
- Change one unit per line and write the new rate each time.
- Round only at the end, and check with a shortcut if there is one.
(i) What is the cost rate?
(ii) What is the cost of \(14\) LED bulbs?
| \(12.50 \div 5\) | \(=\) | \(2.50\) |
| \(14 \times 2.50\) | \(=\) | \(35\) |
(i) \(\$2.50\) per bulb
(ii) \(\$35.00\)
(ii) Change \(540\) mL/min to mL/s.
| \(18 \times 60\) | \(=\) | \(1080\) |
| \(540 \div 60\) | \(=\) | \(9\) |
(i) \(1080\) L/h (an hour is longer, so multiply)
(ii) \(9\) mL/s (a second is shorter, so divide)
| \(750 \times 60\) | \(=\) | \(45\,000\) |
| \(45\,000 \div 1000\) | \(=\) | \(45\) |
Step 1: \(45\,000\) g/h. Step 2: \(45\) kg/h.
| \(12 \times 3600\) | \(=\) | \(43\,200\) |
| \(43\,200 \div 1000\) | \(=\) | \(43.2\) |
\(43.2\) km/h. Check with the shortcut: \(12 \times 3.6 = 43.2\).
(i) Find her average speed in km/h.
(ii) Change this speed to m/s.
| \(1 + 0.5\) | \(=\) | \(1.5\) |
| \(54 \div 1.5\) | \(=\) | \(36\) |
| \(36\,000 \div 3600\) | \(=\) | \(10\) |
(i) \(36\) km/h
(ii) \(10\) m/s (check: \(36 \div 3.6 = 10\))
| \(4200 \div 3600\) | \(=\) | \(1.1666\ldots\) |
\(\approx 1.17\) kg/s
Common pitfalls
Frequently asked questions
How do you change L/min to L/h?
Multiply by \(60\), because an hour has \(60\) minutes. \(18\) L/min is \(1080\) L/h.
How do you change m/s to km/h?
Multiply by \(3.6\). \(25\) m/s is \(90\) km/h.
How do you change km/h to m/s?
Divide by \(3.6\). \(36\) km/h is \(10\) m/s.
How do you convert a rate when both units change?
Change one unit at a time. \(750\) g/min \(= 45\,000\) g/h \(= 45\) kg/h.
How do you write 1 hour 45 minutes in hours?
\(45\) min is \(\dfrac{45}{60} = 0.75\) h, so it is \(1.75\) h.