Here in this post, i will teach the meaning of rates, speed and density and how the three are related. How to solve word problems involving rates, speed and density.
We say that, when we combined two measures, we call such a measure COMPOUND MEASURE. Such compound measures are :
Rates
Speeds
Density, etc.
Rate
Rate are used to compare quantities of different kinds. Example are km/h; N/kg ; km/ l etc. per means "for every".
Examples are
(a) Rate of pay: Used to compare money and time
(b) Gasonline consumption compares distance travelled and amount of fuel used.For example 15km/l.
(c) 15km/l means for every 15km, 1 litre of fuel is used.
Example 1
(1) The price of a car increases from N2 050 000 to N2 500 000 per car. Find the percentage rate of increase.
(2) A truck uses 10 liters of diesel to travel 250km. What is its diesel consumption in km/liter?
Solution
(1) Increases from N2 050 000 to N2 500 000
= N 450 000
On every naira increase rate is
N 450 000
= -------------- = 0.22
N2 050 000
Therefore percentage rate of increase
= 0.22 x 100%
= 22%
The above example illustrated how you can calculate an inflation affecting the price of a car. The the rate is calculated now, that means the increase of 450,000 is 22% of N2 050 000.The insurance if for consumers to know how they can calculate any rate and the percentage of their goods and products.
(2) A truck uses 10 liters of diesel to travel from Uyo to Calabar at 250km. What is its diesel consumption in km/liter?
Let assume the litters of diesel is 10.
250km
1litter is =---------
10
= 25km/l
25km is 1 litter of diesel per km is used by the driver.
Example 2
Speed
The distance travelled in a unit time is the speed of such an object.
(1) If a car travels 100km in 3 hours, what is the speed?
(2) If a horse travels 108km in 3 hours, find
(a) its speed in km/h
(b) its speed in m/s
Solution
1) If a car travels 100km in 3 hours, what is the speed?
Distance 100km
Speed --------- = ---------
Time 3 hours
= 33.333 km /hr
(2a).Speed in km/hr.
108km
-------
3hrs
= 36km/hr
(b) 108km in 3 hours
convert km to m /s
1000m = 108 km
1000m x 108km
108 km -----------------
1
108 000m
1hr(60 x 60) seconds = 3600 seconds
36 x 1000
Speed in m/s ------------
3600
10m/s
Example 3
(1) If a car travelling at speed of 100km/h travels a distance of 240km.Find the time it took for the car to travel that far.
(2) 4 horse running at an average speed of 60km/h runs 45 minutes. How far did it travel?
(3) If a car travel at 1000 meters in 40 seconds, find its speed in
(a) m/s
(b) km/hr
Solution
(1) If a car travelling at speed of 100km/h travels a distance of 240km.Find the time it took for the car to travel that far.
Distance = 240km
Speed = 100km/h
Time = ?
Distance 240km
Time ---------- = --------
Speed 100km/h
= 2.4 hrs
0 .4 x 60
= 24 mins
Time it took = 2 hrs 24 seconds
(2) 4 horse running at an average speed of 60km/h runs 45 minutes. How far did it travel?
45
40 minutes ----- hrs = 0.75
60
Distance = Speed x Time
= 60km/h x 0.75 hrs
= 45 km
(3) If a car travel at 1000 meters in 40 seconds ,find its speed in
(a) m/s
(b) km/hr
Distance
(a)Speed ----------
Time
1000
= --------
40
Speed = 25m/s
(b) Speed in km/h
25
---------- x 3600
1000
= 90 km/hr
Activities
(1) A car travels from Ikeja to Abeokuta 160 km away. If it travels at an average speed of 95 km/h, how long does the journey take the car?
(2) A car travels over 40000 meters in 50 seconds. Find
(a) Its speed in m/s
(b) Its speed in km/h
1
(3) A man runs so 2 ----- hours over a distance of 150km.Find his average speed.
2
With the examples, you solve the activities given, just follow the rules and you are good to go. Please if you have questions, you are free to put them in the comments box.
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