SOLVING PROBLEMS WITH UNIT RATE AND GRAPH

Example 1 :

The graph shows the progress of a train travelling between cities.

a) How far does the train travel in the 4 hour journey?

b) Write down a rate which compares the distance travelled with the time taken.

c)  What was the speed of the train for this journey

Solution :

a) By observing the graph, distance traveled by the train in 4 hours is 240 km.

b) 

Rate  =  Distance travelled / time taken

Rate  =  240/4

=  60

So, unit rate is 60 km.

c)  Speed of the train is 60 km/hr.

Example 2 :

The graph alongside shows how much a student earns for working at a local newsagent.

a) How much does the student receive for working 4 hours?

b) How many hours does the student have to work to earn $18?

c) What is the rate of pay?

Solution :

(a)  By observing the graph, if a person works for 4 hours, he will receive $48. 

b)  Unit rate  =  Total wages/number of hours worked

=  48/4

=  12

Let x be the number of hours he works to get $18.

12x  =  18

x  =  18/12

x  =  3/2

x  =  1.5

So, the student has to work 1.5 hours to earn $18.

c) rate of pay is $12.

Example 3 :

For each 60 km travelled a rally car uses five liters of fuel.

a) Copy and complete the graph opposite.

b) Use the graph to find the distance the car would travel on 20 L of fuel.

c)  How many liters of fuel would be needed to travel 180 km?

d) Join the points on your graph. What do you notice?

e) Use the graph to estimate how far the rally driver could travel on 18 L of petrol.

f)  What is the rate of petrol consumption?

Solution :

(b)  Using 20 liter of petrol the car can travel 240 km.

(c)  From the graph, quantity of petrol used to travel 180 km is 15 liter.

(d)  When we join the points, we get a straight line.

(e)  5 liters of petrol is used to 60 km

Unit rate  =  60/5

=  12 km

Using 1 liter of petrol, they can travel 12 km.

Using 18 l of petrol, they can travel

=  12(18)

=  216 km

So, they can travel 216 km.

f)  Rate of petrol consumption is 12 km.

Example 4 :

Consider the following distance-time graph showing the progress of car travelling from town A to B to C.

a) How far is it from A to B ?

b) How long did it take to get from A to B?

c) What was the speed of the car while travelling from A to B?

d) How far is it from B to C?

e) How long did it take to get from B to C?

f) What was the speed of the car while travelling from B to C?

Solution :

(a)  By observing the graph, distance between A and B is 100 km.

(b) He is taking 2 hours to reach B from A.

(c)  Time  =  Distance/Speed

Here distance  =  100 km, time  =  2 hours

Speed  =  100/5

Speed  =  20 km/hr

(d)  Distance from A to C is 200 km

Distance from B to C  =  200 - 100

  =  100 km

(e)  The car will take 1 hour to reach from B to C.

(f)  Speed taken from B to C  =  100/1

=  100 km/hr

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