FINDING UNIT RATE EXAMPLES

What is unit rate ?

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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