### Chap 9.2 RATE (L3) CONSTANT Rate vs AVERAGE Rate

Here are 2 scenarios:
• The tap in the bathroom leaks - 2 drops of water droplets for every minute. 2 drops of water/minute is considered as "CONSTANT RATE".
• BenoĆ®t Lecomte, the French long distance swimmer was the first man to swim across the Atlantic Ocean at the rate of 43.6 miles in a day. 43.6 miles/day is considered as "AVERAGE RATE".
Are you able to tell the difference between CONSTANT Rate and AVERAGE Rate?
When do we use CONSTANT rate and when to use AVERAGE rate?

[updated on 28 May 2010]:
The above exercise is 'closed'.
11 responses were gathered and the analysis is as follows:

(a) If we assume that the car is travel non-stop at a steady speed (that is, there is no stopping of the car along the way; or it does not become slower or faster at any point of time), the rate of petrol consumption would be constant.
On the other hand, if the car stops along the way and there are occasions when it moves faster or slower, then the rate given would be the average rate.

(b) If we consider the tap is already turned on (before we start to measure) and there is no changes to the rate the water flows from the tap, the rate of water flow should be constant.
On the other hand, if one takes into account TURNING ON the tap to a steady flow of water out from the tap, there would be some changes at the beginning - from 0 litres per minute (i.e. when the tap was closed) to 11.5 litres per minute; then what's indicated would be the average rate.

(c) As the dish washing is handled by a person, there could be instances more time spent to clean up one bowl than a plate, etc. Hence, the rate is average.

(d) The nature of the task (i.e. mountain climbing) would require the climber to take short breaks in-between. Hence, the speed is average.

(e) Based on the context - for such a large land area, it is likely that some machinery or automated system is used to apply the insecticide. Hence, it is highly likely considered constant Rate. Of course, in a developing country, such work will be carried out manually, and since work done by people is highly unlikely at the same rate, then it would be average rate.

(f) The rate is highly likely average rate because one may cycle faster or slower at certain time, or may even take a short break.

(g) If we consider the pipe is already turned on (before we start to measure) and there is no changes to the rate the petrol flows from the tap, the rate of petrol flow should be constant. On the other hand, if one takes into account TURNING ON the pipe to a steady flow of petrol out from the tap, there would be some changes at the beginning - from 0 litres per minute (i.e. when the pipe was closed) to 0.5 litres per second; then what's indicated would be the average rate.

(h) If the change of temperature is managed by some machines, then the rate could be constant.
On the other hand, if it is measurement on the change of temperature of materials (e.g. water) that is subjected to general room enviroment, the rate would be average - since at certain point, the temperature may drop much faster until when it reaches near room temperature.

(i) This is Constant Rate because the payment is fixed - for every one hour the worker works, he would be paid \$9. To find the amount charged after a number of hours, simply multiple by a factor (i.e. \$9)

(j) This is Constant Rate because the monthly rent is fixed - for every square metre, one has to pay \$2.50. To find the amount charged after a number of hours, simply multiple by a factor (i.e. \$2.50) as well as the size of the space rented.

(k) It is average rate - as there are numerous reasons that cause rainforest destroyed, hence the amount destroyed varies from year to year. We know that there is constant effort to protect the rainforest. Hence, there would not be 'intended' target for the amount of rainforest destroyed.

(l) This is average rate - as there is no control over the number of babies are born.

(m) This is average age - as there are many factors to the decrease of population (e.g. migration, death) and these are non-controllable factors.

(n) This is constant rate as it's controlled by the machine.

(o) This is Constant Rate because the charges is fixed for each kWh. To find the amount charged, simply multiple by a factor (i.e. 20 cents)

(q) This is Constant Rate because the charges is fixed for each cubic metre of water. To find the amount charged, simply multiple by a factor (i.e. \$1.20)
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Enter your thoughts on the difference between CONSTANT Rate and AVERAGE Rate in COMMENTS.

1. Average speed allows you to change the instantaneous speed throughout the travel time, while during constant speed, one keeps the instantaneous speed at the same.

Constant Rate means that an object is travelling at the same speed throughout.
Average Rate means that an object may not be at the same speed. Average speed is the distance divided by the time.

JJ(:

2. Average rate is calculated by taking the total amount divided by the total number of times, etc. Whereas for constant rate, it means the rate remains the same through out the period of time.

E.g. The birth rate of the country is 18.4 babies per 1000 people is an average rate because within the 1000 people, some might have given birth to 1 child while some might have given birth to 2 or more children. The data is gained by calculating the average rate. In this case, taking the total number of babies born divided by 1000 people.

Because the number of children given birth by each of the 1000 people is different, the data cannot be considered as a constant rate.

3. Constant rate represents a quantity that is constant throughout.
e.g. A printer prints at the rate of 12 pages per minute; the machine will always remain operating at this rate.

Average rate represents a quantity that may be different at certain periods of time but are averaged out.
e.g. The population of a city was decreasing at the rate of 15000 per year for the past 10 years; maybe in the first year the population of the city decreased by 12000, however perhaps in the second year the population of the city decreased by 10000. So "The population of a city was decreasing at the rate of 15000 per year for the past 10 years" is just an average added together over 10 years.

4. To Jing Jie, Ziying and Jianhui: Good interpretation :D

5. Good use of google form:)