USING UNIT RATES TO SOLVE PROBLEMS

Some rates are constant whereas others vary with time. For example, we know the speed of a car varies as we accelerate or brake.

If a rate remains constant over time then we can use this to solve problems.

Problem 1 :

Water consumption for a person living in Sydney is approximately 2100 liters per week. At this time, how much water would be used by a person in two days ?

Solution :

Water consumption per week  =  2100 liters

Water consumption per day  =  2100/7

=  300

Water used in one day  =  300(2)

=  600 liters

Problem 2 :

Bill is a part time curator at the local cricket ground. He earned \$169.60 for working 8 hours last week. This week he has worked 21 hours. How much will he earn this week if he is paid at the same hourly rate?

Solution :

His earning for 8 hours  =  169.60

His earning in 1 hour  =  169.60/8

=  21.2

His earning for 21 hours  =  21 (21.2)

=  445.2

Problem 3 :

A petrol tanker takes 18 minutes to discharge 8100 liters of fuel.

a) At this rate, how much fuel would the tanker discharge in 14 minutes ?

b) How long would it take the tanker to discharge 4950 litters of fuel at the same rate?

Solution :

Time taken to discharge 8100  liters of fuel  =  18 minutes

So, in 1 minute it will discharge  =  8100/18 liters

=  450 liters

Problem 4 :

A motor vehicle can travel 84 km on 7 liters of petrol.

a) How far could the vehicle travel on 57 liters of petrol?

b) How many liters of petrol would be required to travel a distance of 420 km?

Solution :

Distance covered using 7 liter of petrol  =  84 km

Distance covered using 1 liter of petrol  =  84/7

=  12 km

Let x be the required quantity of petrol to be used to cover the distance of 420 km.

x  =  420/12

x  =  35

So, required quantity of petrol to cover 420 km is 35 l.

Problem 5 :

It costs \$2340 to lay a drain pipe of length 36 m.

a) Find the cost of laying a drain pipe of length 63 m.

b) Find the length of pipe that could be laid for a cost of \$7540.

Solution :

Cost spent to lay drain pipe of length 36 m  =  2340

Cost spent to lay drain pipe of length 1 m  =  2340/36

=  65

Cost spent for laying a drain pipe of length 63 m

=  65(63)

=  \$4095

Let x be the required length of pipe that could laid for the given cost

x  =  7540/65

x  =  116

So, required quantity of pipe is 116 m.

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