Solving Problems Involving Rational Equations





At the end of the lesson the students are expected to:

1. Gain skill in solving work and motion problems.

2. Understand the techniques in solving work and motion problems.

3. Gain skill in manipulating rational equations.

4. Gain ability in analyzing and solving Algebra Word Problems.

INTRODUCTION: Why a lesson in solving rational equation?

Rational Equations is one of the most important concept in Algebra. This subject has sought many great applications in many fields of Mathematics.

In Trigonometry, applications involving solving oblique triangle require the use of rational equation. The Law of Lines, the Law of Corines and Law of Tangents are usually expressed as a rational equations.

In Physics, majority of the application problems involve rational equations. Most of the problem in Mechanics involve skill in manipulation of rational equations.

May it be a problem involving motion or force, it requires skill in handling rational equations.

In Mathematics of Investment, applying the concept of rational equations remains inevitable. Problems in interest and discount require skills in handling rational equations.

In fact, all fields of Mathematics requires handling of rational equations. Next to linear equation, I believe firmly that The concept of “Rational Equations” is the most important concept in Algebra.


Part One:

Problem Involving Work

Problem Number One:

Leonor mows a lawn in 4 hours Alex can mow the same lawn in 5 hours. How long would it take both of them, working together, to mow the lawn.


In solving this problem, one consider first how much of the job is done in one hour, two hours and so on.

It takes Leo 4 hours to mow the entire lawn . Thus after one hour, he has done ¼ of the lawn. It takes Alex 5 hours to mow the entire lawn. Thus after one hour he has done 1/5 of the entire lawn.


Let t = the number of hours it will take both Leo and Alex

to finish the lawn working together

Working equation:

t (1/4 + 1/5) = 1

(t/4 + t/5 = 1) 20

5t + 4t = 20

9t/9 = 20/9

t = 20/9 or 2 and 2/9 hours

Answer : 2-2/9

Sample Problem Two:

It takes Ramil 9 hours longer to construct a fence than it takes Ency. If they work together, they can construct the fence in 20 hours. How long would it takes each working along to construct the fence?



Let t = the amount of time it would take Ency working alone.

t + 9 = the amount of time it would take Ramil working alone

Using the same reasoning in the previous problem, we can assume then that Ency has finished 1/t of the fence after one hour and Ramil has finished 1/t+9 of the fence after one hour. Since Ramil and Ency can complete the entire fence in 20 hours, we have:

20 (1/t + 1/t+9) = 1

as our working equation:

20/t + 20/t+9 = 1 LCM: (t) (t + 9)

(t) (t + 9) (20/t + 20/t+9) = 1 (t) (t + 9)

(t + 9)20 + t . 20 = (t) (t + 9)

20 + 180 + 20t = t2 + 9t

40T + 180 = t2 + 9t

0 = t2 – 31t – 180

(t – 36) (t + 5) = 0

t – 36 = 0 t + 5 = 0

t = 36 t = -5

It takes 36 hours for Ency to do the fence alone and it takes 45 hours for Ramil to do the work alone.

Check: 20/36 + 20/45 = 1

5/9 + 4/9 = 1

9/9 = 1


Sample Problem:

Biker A bikes 15 faster than Biker B. By the time it takes Biker A to reach 80 km. Biker B has gone 50 km. Find the speed of each biker.



Let r = The rate in km/hr. of biker B

r + 15 = the rate in km/hr of Biker A

Distance Speed Time

A 80 r + 15 t

B 50 r t

Since time = distance/rate

Distance Speed Time

A 80 r + 15 80/r+15

B 50 r 50/r

From the problem, it is given that the time is the same, we can now have our working equation as:

50/t = 80/r+15

r (r+15) = 50/r = 80/r+15 = (r) (r+15)

50 (r+15) = 80R

50r + 750 = 80r

750 = 80r – 50r

750 = 80r – 50r

750/30 = 30r/30

r = 25

Biker B is going at 25 km/hr. and Biker A’s speed is 40 km./hr.


Mastering Intermediate Algebra

by: Simon L Chua

Benson S. Tan

Roberto G. Degolacion

Ma. Salome B. Aguinaldo

We are offering tutorial services for Mathematics subjects, Physics and Chemistry.. Just email for your tutorial needs.

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Comments 108 comments

eovery profile image

eovery 7 years ago from MIddle of the Boondocks of Iowa

Good explanation.

Duck soup,

Keep on Hubbing!

Melody Lagrimas profile image

Melody Lagrimas 7 years ago from Philippines

Thanks for this mathematics refresher.:). Great presentation.

Kurt 7 years ago

ejeu! estoy en el CIDEB :D :P nice explanation ddddd:P

steph 7 years ago

oh wow its very clear nice one

leethepanda 6 years ago

I LOVE YOU thank you so much

ken 6 years ago

thanks your solution really helped for me to understand how to solve it, its really clear and great job!

ken 6 years ago

thanks your solution really helped for me to understand how to solve it, its really clear and great job!

secret 6 years ago


cath 6 years ago

thank you. :)

Wouie Pajo 5 years ago

Thanks for the answer.! GOD bless you!

ann 5 years ago

thanks a lot.. helpful talaga sya..

jacob 5 years ago

thank' you are kind

shenie bolina 5 years ago

it so beautiful,thanks because i learned more,,,:P

katrina 5 years ago

nice, i have my assignment for tomorrow !:


camille 5 years ago

thansks for this answer so now i can pass my assignment and ihave a high grade!!!!!!!!!!!!!!!!???????????

dwight 5 years ago

thank you

rhose 5 years ago

great! a big help for me

michelle 5 years ago


angel 5 years ago

tnx. for that solution,cause i have passing project tommorow....thank you very much....

john alexis cruz 5 years ago

tnx p0h tlga sa mga answer helpful p0h tlga cea sana marami ka pang matulungan

frozen_fire 5 years ago

can I post my problem too?.

jessa mae realista 5 years ago

thank you po 5 years ago

nice one it helps me very much!!!

karl_18 5 years ago

pede po ba padagdag ng example ng lima papo kasi po kulang e ty

jochelle matibag 5 years ago

. thankz 4 that solution ..

. mkakapasa na ako ng project nmin !

thanz so much tlaga :)

qwerty 5 years ago

tenx poh

elina gilbert 5 years ago

hahaha.. very simple....

mhayla 5 years ago

nakatulong po kau sa project namin salamt

JOSEPH 5 years ago

THANKS!! 5 years ago

thanks po.dahil d2 nagawa ko po ung project ko.......

mark joseph pili 5 years ago


loves 5 years ago


Michael Coronejo 5 years ago

It helps to do my Assignment! :) In tagalog: nakatulong ito na magawa ang aking assignment!

donna ogayre 5 years ago

i love mathematics... nice presentation

donna 5 years ago

thanks i have my project tomorrow... i feel great!

jhAnexz 5 years ago

yEhey ntpOx kOh nAh riN prOjeCt hehe :)

i lOve iT!!!!

soniya 5 years ago

as part of the 'learning jorney'programs ,73 pupils travelled on two buses ,one air-contioned and other one non-air-conditioned, to the sinapore Discovery Center.Three-fifths of the pupils on the aie conditioned bus were girls .There were !7 boys in the non_air-conditioned bus.The nimber of girls on the two buses were equal.How many pupils were there on the air - conditioned bus? can saome anser this questin

lydia 5 years ago


archiel 5 years ago

.tnx pow tlega hah! it help me soooooooooooo. much!...

rutine 5 years ago

tnx sa word problem kc project ko ito eh tnx. tlga nakatulng ng mlki

sai 5 years ago

nand2 tlaga ung hinihanap k0 per0,, ung ubang problem wlang checking...

CHA 5 years ago

yes nakita na jud ko sa answer


danielle 5 years ago

yun oh..! yun plah yon..! ahhaha

margie 5 years ago

thank you po because you help all the students how to solve in math easily

maria 5 years ago


Angelo_4 5 years ago

Like This

jhesa 5 years ago

tnz po

joanne 5 years ago

yay! project finish!

M.sailaja 5 years ago

verrrrry simple nd sweet

irish paola ave 5 years ago

thank you po sa gnwa nio po it so very expensive and valuable

chronous_03 5 years ago

tanx!!!!!1sa problem sana marami pa don!!!

ella dapiton!!! 5 years ago

thank you for posting this!!! because you can help student how to solve this problem!!

jimwellustares 5 years ago

thank you for some informations in math

i hope you will have more!!!!

jessie mendoza 5 years ago

thank you for helping me :) keep up the best in u

rose 5 years ago

thank very much

yancelyn 5 years ago

thank u for helping me to my homework^_^ salamat poh talaga!!!!!!!!!!!!!!!!!!!!!!!

hazzel grace 5 years ago

salamat dahil dito kulang nalaman ang lhat ng sagot sa assignment ko txnsssssss pohhhhhhh tlga::::::::::::: )))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) thank uuuuuuuuuuuuuu

bryan 5 years ago

thank u poh


jheiain yuri lee 5 years ago

tnx for the explanation....

nice one,..:P

carsel 5 years ago


anne 5 years ago

thank u...for posting this....yezzz... now i can answer my assignment......tyhankzzzzz u.... tlga....,.,.,.

gero gamarcha 5 years ago

its very nice that you make this math. i love math

vanessa jirah aparece 5 years ago

thanks a lot.........

tine:)) 5 years ago

thanks makakapasa na kmi:))

ruth=) 5 years ago

thanks a lot....

because i made it as a project....hehehhee

janice j. vasquez 5 years ago

2 too nga

joyce 5 years ago

thanks po

joyce 5 years ago

grabe thanks po

ang ganda wow

my project n q kaso unti nga lang

Alexandria 5 years ago

thank you very muchhhh xDD

analyn 5 years ago

thanks a lot

prince 5 years ago



EE ..

kimberly 5 years ago


Thank For That samples and for that explanation :D

rilina 5 years ago

thanks very much!kso 15 ang kailingan ko eh


aileen 5 years ago

yes i have my project thank you pho

happy Valentine's Day pho

Mark 5 years ago

I just want to have an example of problem all about rational equation because it is our project in math and I learned many things here and a happy valentines to all

PINOY 4 years ago


kenth 4 years ago

makakagawa na me ng project....thank a lot

chai merced 4 years ago

thank you sooo much,you help me a lot

mae 4 years ago


kathy 4 years ago


secret 4 years ago

gok ala kuang abalu

MR.III 4 years ago

salamat sa tulong!

sky.ramz 4 years ago



jasper magtuloy 4 years ago

wala akong nakita sa tanung ko AA??!!!

alfred 4 years ago

thank u poh

nikka 4 years ago

thanks a lot... nakapag pasa na ako ng PROJECT ko... maraming theynk you poh talaga!!!!!!

50 petot 4 years ago

yesssssssss!!!! maraming salamat

cLifForD 4 years ago

thank a lot.......nakapag pasa ako ng project ko.....maraming thank you

Navi Ramirez 4 years ago

bakit po dalawa lang? bakit ndi kumpleto.

bhea 4 years ago

anggggggggggg hirrrrrraaaaaaaaaaaapppppppppppp

almarie 4 years ago

thank you

jhaylyn 4 years ago

dapat po marami para may sagot na ako hehehehehehe

thank kasi nakagawa ako ng ass. ko dahil sayo 4 years ago


ryan 4 years ago

pwede dagdag pa ng example

Patricia nicole 4 years ago

thanks pero sana dagdag pa po ng example kaxi kailangAN sa project koeh... pero thank you po talaga sa inyo

God bless you..!!:)

mae2 4 years ago

thank you know i have my assingment....nxt time again:)

Mee 4 years ago

thankss .. now gets kuna !! :)

angel 4 years ago

thakz !!!

justine marie clarisa 4 years ago

thank u!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

pearl_Qleim 4 years ago

thanks a lot !!!

ice cube 4 years ago

yo thanks

darwin 4 years ago

mlapit ng matapos ang proj. ko dhil dto.......slamat....!!!!!!!

NO NAME ^_^ 4 years ago


money 3 years ago

wouldn't (t)(t) equal t^2 not 2t in the second problem of the part one?

zaf1074 3 years ago

its clear and good

john mhel 3 years ago

thnks po..... may projct na ako

ken marce 3 years ago

thangk u for this now i can pas my project

anne 17 months ago

Tnx po xa mga problem na binigay.... God Bless

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