|
| Ratios and Proportions
|
|
|
|
Inverse proportion
|
|
Graphical representation of inverse
proportionality
|
|
Coefficient of inverse
proportionality
|
|
Inverse proportion practice
problems |
|
|
|
|
|
|
| Inverse proportion
|
| The two related variable quantities
x and
y whose product is
constant i.e., |
| |
x
· y = k
or |
 |
are
inversely proportional. |
|
|
| That is, related quantities are inversely proportional
when an increase by a certain multiple in one, brings about or is
associated with, a decrease by the same factor in the other. |
| By whatever ratio one quantity changes, the other will change in the
inverse ratio. |
| This means that if one of the quantities triples, then
the other will become one third as large. |
|
| Graphical representation of inverse
proportionality
|
| If
x and
y are inversely proportional quantities, i.e.,
x
· y = k then,
the same relationship holds between their corresponding values
x1,
y1 and
x2,
y2. |
| Therefore,
x1
· y1 = k
and
x2
· y2 = k
that is,
x1
· y1 =
x2
· y2. |
| Dividing by
x2
· y1 gives the proportion |
 |
or |
x1
:
x2 =
y2
:
y1 |
|
 |
|
|
| Inverse proportion practice
problems |
| Example:
If 12 workers can do a job in 15 hours, then how many workers
would be needed to do the job in 9
hours?
|
| It’s obvious that more workers will do a job in shorter time. That
means, the time it takes to do the job is inversely proportional to the
number of workers. |
|
12
|
 |
x1 |
|
 |
y1 |
|
|
| x2 |
y2 |
or |
x1
:
x2
=
y2
:
y1 |
|
| |
|
12
workers |
|
|
15
hours |
|
|
| Thus, |
x
workers |
|
9
hours |
or |
12
:
x =
9 :
15 |
|
| |
|
|
| => |
 |
workers. |
|
|
|
| Example:
A distance
d
from place A to place B a car covers in 75 minutes
traveling at the rate of 120 km/h. |
| At what rate it should drive so that
it will travel the same distance in 60 minutes. |
| By driving two times
faster, the same distance it will cover in half less time. |
| Since, rate
r and time
t are inversely proportional quantities use the proportion
x1
:
x2 =
y2
:
y1. |
| As the quantities we are comparing must always
be measured in the same units, we’ll convert minutes to hours, |
|
so 75 min =
75
min
· 1hour
/ 60
min =
1.25
h. |
| In the given example the
distance is constant called coefficient of inverse
proportionality. |
| |
|
1.25
h |
|
|
120
km/h |
|
|
| Thus, |
1
h |
|
x
km/h |
or |
1.25
:
1
= x :
120 |
|
| |
|
|
| => |
 |
km/h. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Beginning
Algebra Contents B |
|
|
 |
|
| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
