What is unit rate ?
A unit rate is a rate with 1 in the denominator.
Example 1 :
35 apples bought for $9.45 is at a rate of ...... cents per apple.
Solution :
Cost of 35 apples = $9.45
Cost of 1 apple = 9.45/35
= 0.27
So, cost of 1 apple is 27 cents.
Example 2 :
My car uses 18 L of petrol every 261 km. The rate of petrol consumption is ...... km per litre.
Solution :
Petrol consumption for 261 km = 18 L
That is,
18 L is used to cover 261 km
1 liter petrol is used to cover how much distance.
= 261/18
= 14.5 km
1 liter petrol is used to travel 14.5 km
So, the rate of petrol consumption is 14.5 km per liter.
Example 3 :
675 litres of water are pumped into a tank in 25 minutes. This is a rate of ...... litres per minute.
Solution :
Quantity of water pumped into a tank in 25 minutes
= 675 liters
Quantity of water pumped into a tank in 1 minute
= 675/25
= 27
So, 27 liter of water can be pumped in 1 minute.
Example 4 :
A cyclist travels 120 km in 5 hours. This is a rate of ...... km per hour.
Solution :
Distance covered by cyclist in 5 hours = 120 km
Distance covered by him in 1 hour = 120/5
= 24 km
So, the required rate is 24 km per hour.
Example 5 :
Trevor’s car uses 16 litres of fuel to travel 240 km. Jane’s car uses 12 litres to travel 204 km.
a) Find the rate of fuel consumption in km per L for each car.
b) Which car is more economical to run ?
Solution :
(a)
Trevor's car :
16 liters of fuel is used to travel 240 km
1 liter petrol is used to travel = 240/16
= 15 km
The rate of fuel consumption for Trevor's car
= 15 km per hour
Jane's car :
12 liters of fuel is used to travel 204 km
1 liter petrol is used to travel = 204/12
= 17 km
The rate of fuel consumption for Jane's car
= 17 km per hour
Jane's car is covering more distance using 1 liter of petrol.
(b) Jane's car is more economical.
Example 6 :
Mandy earns $144 for 8 hours’ work. Dzung earns $210 for 14 hours’ work.
a) Find the rate of pay in $ per hour for each person.
b) Who gets paid the better hourly rate?
Solution :
(a)
Mandy is earning $144 in 8 hours
Mandy's earning in 1 hour = 144/8
= $18
Dzung is earning $210 in 14 hours
Dzung's earning in 1 hour = 210/14
= $15
Mandy is getting better hourly rate.
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