REAL-LIFE PROBLEMS:

RATIONAL FUNCTIONS,
EQUATIONS, AND INEQUALITIES
Chapter 2: Rational Functions
 Objectives
1. M11GM-Ib-1: represents real-life situations using rational
functions
2. M11GM-Ib-2: distinguishes rational function, rational equation,
and rational inequality
3. M11GM-Ib-3: solves rational equations and inequalities
4. M11GM-Ic-3: solves problems involving rational functions,
equations, and inequalities
● carefully analyze and understand word problems before solving
● create real-life word problems about rational functions,
equations and inequalities
01
Examples
Rational Functions,
Equations, and Inequalities
in Real Life
 a. How long does it take Mario to reach
school considering his average speed?

Speed it Up! b. If x represents the time it takes Mario to

drive to school with the given distance of 15
km, how will you represent the relationship
of his speed (y) versus the time (x)?
Speed it Up!
Question
a. How long does it
d take Mario to reach
school considering his
average speed?
s t
 Speed it Up!
Question
15km a. How long does it take
Mario to reach school
d considering his average
30km speed?
x
s t x=15/30
x=1/2
 Speed it Up!
Question
b. If x represents the time it
15km
takes Mario to drive to school
d with the given distance of 15
km, how will you represent the
x relationship of his speed (y)
y
versus the time (x)?
s t
 Speed it Up!
Question
b. If x represents the time it
15km
takes Mario to drive to school
d with the given distance of 15
km, how will you represent the
x relationship of his speed (y)
y
versus the time (x)?
s t
y = 15/x
Speed it Up!
Question

c. Mario’s average speed as 30 kilometers per

hour. Suppose Mario lowers his speed by
10km/h, how long will he reach the school
given the same distance?
Speed it Up!
Question
c. Mario’s average speed as 30
kilometers per hour. Suppose
Mario lowers his speed by
10km/h, how long will he reach
the school given the same
distance?
Speed it Up!
Question
d. Suppose Mario’s speed is unknown and
represented by (x), he lowers his speed by 10
km/h at a distance of 15 km and reaches
school at ¾ hours, how will you write the
equation to find his average speed (x)?
 Speed it Up!
Question
d. Suppose Mario’s speed is
unknown and represented by (x),
he lowers his speed by
10 km/h at a distance of 15 km
and reaches school at ¾ hours,
how will you write the equation
to find his average speed (x)?
Speed it Up!
Question
e. Mario’s average speed was 30km/h. He
plans to drive for another 30 km from
school, how long will it take him to cover the
whole distance (house to school to 30 km
from school)?
Speed it Up!
Question
e. Mario’s average speed was
30km/h. He plans to drive for
another 30 km from school,
how long will it take him to
cover the whole distance
(house to school to 30 km
from school)?
Speed it Up!
Question
f. If Mario drives another (x) km from his
school at an average speed of 30 km/h and
he plans to drive in at most 2 hours from his
house, how will you write the inequality to
find the additional distance?
Speed it Up!
Question
f. If Mario drives another (x)
km from his school at an
average speed of 30 km/h and
he plans to drive in at most 2
hours from his house, how will
you write the inequality to find
the additional distance?
 Example #1
Bamban National High 1. Construct a function C(n)
School is preparing for its which would give the
25th founding anniversary. amount of money each of
The chairperson of the
the n numbers of
activity allocated
committees would receive.
₱90,000.00 from different
stakeholders to be divided 2. If there are six committees,
among various committees how much would each
of the celebration. committee have?
 Example #1
Bamban National High Construct a function C(n) which
School is preparing for its would give the amount of money
25th founding anniversary. each of the n numbers of
The chairperson of the committees would receive.
activity allocated
₱90,000.00 from different
stakeholders to be divided
among various committees
of the celebration.
 Example #1
If there are six committees, how
Bamban National High
much would each committee
School is preparing for its
have?
25th founding anniversary.
The chairperson of the
activity allocated
₱90,000.00 from different
stakeholders to be divided
among various committees
of the celebration.
 Example #2
1. Write an equation
Brgy. Masaya allocated ₱100,000 representing the relationship
to provide relief goods for each of the allotted amount per
family in the barangay due to the family (y-variable) versus the
Covid-19 pandemic situation. The total number of families (x-
amount is to be allotted equally variable).
among all the families. At the 2. How much will be the amount
same time a philanthropist of each relief packs if there
allotted an additional ₱500 to be are 200 families in the
received by each family. barangay?
 Example #2
Brgy. Masaya allocated ₱100,000 Write an equation representing
to provide relief goods for each the relationship of the allotted
amount per family (y-variable)
family in the barangay due to the
versus the total number of
Covid-19 pandemic situation. The families (x-variable).
amount is to be allotted equally
among all the families. At the
same time a philanthropist
allotted an additional ₱500 to be
received by each family.
 Example #2
Brgy. Masaya allocated ₱100,000 How much will be the amount of
to provide relief goods for each each relief packs if there are
200 families in the barangay?
family in the barangay due to the
Covid-19 pandemic situation. The
amount is to be allotted equally
among all the families. At the
same time a philanthropist
allotted an additional ₱500 to be
received by each family.
 Example #3
Let x represent the
Vincent discovered his love of
planting vegetables during
width of his garden
quarantine. He found that the in meters, express
area of his rectangular garden is the length of the
200 square meters. garden L as a
function of width x.
 Example #3
Let x represent the width of his
Vincent discovered his love of garden in meters, express the
planting vegetables during length of the garden L as a
quarantine. He found that the function of width x.
area of his rectangular garden is
200 square meters.
Example #4
Rodalyn can do a job in 5 days while Apple
can do the same job in 3 days. How long will
it take them to do the job if they work
together?
 Example #4
Rodalyn can do a job in 5 days
while Apple can do the same
job in 3 days. How long will it
take them to do the job if they
work together?
Alternate solution:
 Example #4 Work
Work = (Rate)(Time)

Rate Time

Rodalyn 1 1/5 5
Rodalyn can do a job in 5 days
while Apple can do the same Apple 1 1/3 3

job in 3 days. How long will it Together 1 (1/5)+(1/3) x

take them to do the job if they

work together?
Example #5
We have a pool that is filled to the top. One
pipe can fill the pool in 20 minutes while
the drain pipe can drain the pool in 15
minutes. If both pipes are opened, how long
will it take to empty the pool?
Example #6
Two pumps can fill a pool in 6 hours. Pump
A can fill the pool 5 hours faster than Pump
B. How long can each pipe fill the pool if
they work alone?
 Example #7
How many liters of
pure alcohol must be
added to 30 liters of
20% alcohol solution
to make a 25%
alcohol solution?
 Original Added Result

Example #7 Concentration
20/100
20%
1
100%
25/100
25%

Amount 30 liters x 30 + x
How many liters of pure (20/100) (1)(x) (25/100)
Multiply
alcohol must be added to 30 (30) (30+x)

liters of 20% alcohol solution

to make a 25% alcohol
solution?
 Example #7 Original

20/100
Added

1
Result

25/100
Concentration
20% 100% 25%
How many liters of pure Amount 30 liters x 30 + x
alcohol must be added to 30
(20/100) (1)(x) (25/100)
liters of 20% alcohol solution Multiply
(30) (30+x)
to make a 25% alcohol
solution?
Example #8

The difference of thrice a number and six,

divided by three is less than or equal to five.
Find the number/s?
Example #9
Kate and Pete play a swimming race every
weekend. So far, Kate has won 7 out of 10
matches. How many matches should Kate
win in a row to improve her winning
percentage to 80%?
Example #10
A box with a square base has a volume of 27
cubic inches. If x is the length of its edge and h
is the height of the box. What are the possible
measurement of its edge if the height should
be longer than the edge?
Example #10
A box with a square base has a
volume of 27 cubic inches. If x
is the length of its edge and h
is the height of the box. What
are the possible measurement
of its edge if the height should
be longer than the edge?
Example #10
A box with a square base has a
volume of 27 cubic inches. If x
is the length of its edge and h
-3 0 3 6
is the height of the box. What
are the possible measurement
of its edge if the height should
be longer than the edge?
✓ X

x<3 0<x<3
For further questions:

messenger.com/t/chrishakate.dimapilis
Chapter 2,
Lesson 10 done!
chrishakate.dimapilis@depedqc.ph
+639 17 167 0362
bit.ly/eduKate-ph

Try it on your own now! :D