Other contexts
Rates are used in a variety of places in households (rates of water flow), agriculture (fertilisers and seeds), business management (flow of customers) and the list goes on.
Practice questions
Question 1
Dave can wash $2$2 cars in $4$4 minutes.
How long would it take for him to wash 1 car?
How long would it take him to wash $20$20 cars?
Question 2
The height of a pool increases by $5$5 cm for every $10$10 litres of water added.
After adding some water the height of the pool increased by $0.45$0.45 m.
How many groups of $5$5 cm are there in $0.45$0.45 m?
How much water was added to the pool?
Question 3
In $2011$2011, the literacy rate in Cuba was $98$98 people for every $100$100 in the population. This is the rate of the population aged $15$15 and above who can, with understanding, read and write a short, simple statement on their everyday life. For a town with a population of $83000$83000, how many literate people would you expect?
Heart rates
A person's pulse rate is normally given as a number of beats per minute. However, when measuring someone's pulse, a medical practitioner usually does not want to count the number of heart beats over a full minute.
Instead, it is more convenient to count the number of beats in a shorter time, say, $15$15 seconds and then to use this number to predict how many beats there would be in a full minute.
Thus, if $14$14 beats were counted in a period of $15$15 seconds, we would argue that since there are $4$4 lots of $15$15 seconds in a minute we must multiply the $14$14 by $4$4 and get $56$56, the number of beats that would occur per minute.
Another approach would be to measure with a stopwatch the time taken for a fixed number of heart beats, say $10$10, and to use this time measurement to work out the rate per minute.
Worked example
EXample 1
After sleeping, a person's heart was found to beat $12$12 times in $15$15 seconds. What is their heart rate in beats per minute?
Think: How many periods of $15$15 seconds are there in $60$60 seconds. The number of beats per minute will be $10$10 times this number.
Do: Calculate $\frac{60}{15}\times12=48$6015×12=48 beats per minute.
Heart rates are a rate of pulse beats per unit of time.
The most common measure is beats per minute.
Practice question
Question 4
A pulse was recorded beating at $11$11 times per $10$10 seconds. How many beats per minute is this?