Understanding Rates
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About Understanding Rates
In these notes you are going to be able to practice Rates related exercises when calculating and solving questions. Make sure to practice all the questions so that you get used to solving problems of this nature.
Note that “Understanding Rates” is a sub topic and you can also access more notes, questions and answers under the main topic “Operations On Numbers And Calculator Skills” which is one of the recommended learning topics in the NSC (CAPS) Mathematical Literacy curriculum.
Understanding Rates
What is a Rate
A rate is a specific type of ratio that compares two quantities of different units, showing how one quantity changes in relation to another over a specified period or distance. For example, speed is a rate that compares distance traveled to the time taken (Kilometers per hour). In contrast, a ratio is a broader term that compares two quantities of the same unit, indicating their relative sizes. For instance, the ratio of 3 to 2 in a classroom means there are 3 boys for every 2 girls. While all rates are ratios, not all ratios are rates, as rates specifically involve different units.
Distance, Speed and Time
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Mixed Exercises
1. The cost of water is R11.72 per kl(kiloliter).
1.1 Determine the expense for 342 liters of water.
1.2 What is the volume of water consumed if the water bill amounts to R164.08?
2. Given that a car can travel 500 km on a 35-liter tank of petrol, determine the car’s fuel consumption per 100 km.
3. Casandra commutes 25 km to her workplace daily. If her travel time is about 33 minutes, determine her approximate speed in kilometers per hour (km/h).
4. A turkey requires 30 minutes of roasting time for every 500 grams of meat. What will be the total roasting time for a turkey that weighs 1.2 kg?
5. A family heading on a weekend trip is driving at 120 km/h on the N2. They are currently 160 km from their destination. How long will it take them to arrive at their destination? Please provide your answer in hours and minutes.
6. Which of the three products sold at Pick N Pay is the most expensive?
- Chocolate Yogurt (175 ml) for R89.99
- Sta Soft (180 ml) for R92.99
- Vanilla Custard (150 ml) for R70.99
Answer:
1.1
Number of kilolitres = 342l ÷ 1 000 = 0,342 kl
Cost = R11,72 x 0,342 kl = R4,00
1.2
Number of kilolitres = R164.80 ÷ R11.72 = 14 kl
500 km on 35 L
= 100 km on 35÷5 = 7L
= 7L per 100 km
3.
Number of hours = 33 minutes ÷ 60 = 0,55 h
\[Speed=\frac{dis\tan ce}{time}\\=\frac{25\;km}{0,55h}\\=\;45,45\;km/h\]
4.
time : weight
30 min : 500 g
Hint: divide both sides by 500
0,06:1g
?: 1 200 g
Hint: Convert all units to the smallest common unit, which is grams in this case: 1.2kg x 1,000 = 1,200g
Time = (30 min + 500) x 1 200 g
= 72 min
\[Time=\frac{dis\tan ce}{speed}\\=\frac{160\;km}{120km/h}\\(Hint:\;\\Convert\;to\;minutes:\;multiply\;by\;60\\0,33x60\;=\;20\;minutes)\\=1,33\;h\\=1h\;and\;20\;min\]
6.
Chocolate Yogurt: R89,99÷175 ml = R0,514/ml
Sta Soft: R92,99÷180ml= R0,516/ml
Vanilla Custard: R70,99÷150ml = R0,473/ml
Sta Soft is the most expensive face cream
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