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Solving Problems Involving Rational Equations

Updated on November 17, 2011





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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    • profile image

      anne 2 years ago

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

    • profile image

      ken marce 4 years ago

      thangk u for this now i can pas my project

    • profile image

      john mhel 4 years ago

      thnks po..... may projct na ako

    • profile image

      zaf1074 5 years ago

      its clear and good

    • profile image

      money 5 years ago

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

    • profile image

      NO NAME ^_^ 5 years ago


    • profile image

      darwin 5 years ago

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

    • profile image

      ice cube 5 years ago

      yo thanks

    • profile image

      pearl_Qleim 5 years ago

      thanks a lot !!!

    • profile image

      justine marie clarisa 5 years ago

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

    • profile image

      angel 5 years ago

      thakz !!!

    • profile image

      Mee 5 years ago

      thankss .. now gets kuna !! :)

    • profile image

      mae2 5 years ago

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

    • profile image

      Patricia nicole 5 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..!!:)

    • profile image

      ryan 5 years ago

      pwede dagdag pa ng example

    • profile image

      thank kasi nakagawa ako ng ass. ko dahil sayo 5 years ago


    • profile image

      jhaylyn 5 years ago

      dapat po marami para may sagot na ako hehehehehehe

    • profile image

      almarie 5 years ago

      thank you

    • profile image

      bhea 5 years ago

      anggggggggggg hirrrrrraaaaaaaaaaaapppppppppppp

    • profile image

      Navi Ramirez 5 years ago

      bakit po dalawa lang? bakit ndi kumpleto.

    • profile image

      cLifForD 5 years ago

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

    • profile image

      50 petot 5 years ago

      yesssssssss!!!! maraming salamat

    • profile image

      nikka 5 years ago

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

    • profile image

      alfred 5 years ago

      thank u poh

    • profile image

      jasper magtuloy 5 years ago

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

    • profile image

      sky.ramz 5 years ago



    • profile image

      MR.III 5 years ago

      salamat sa tulong!

    • profile image

      secret 5 years ago

      gok ala kuang abalu

    • profile image

      kathy 5 years ago


    • profile image

      mae 5 years ago


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      chai merced 5 years ago

      thank you sooo much,you help me a lot

    • profile image

      kenth 5 years ago

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

    • profile image

      PINOY 6 years ago

      PROJECT (ACCOMPLISHH) wahahhahah

    • profile image

      Mark 6 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

    • profile image

      aileen 6 years ago

      yes i have my project thank you pho

      happy Valentine's Day pho

    • profile image

      rilina 6 years ago

      thanks very much!kso 15 ang kailingan ko eh


    • profile image

      kimberly 6 years ago


      Thank For That samples and for that explanation :D

    • profile image

      prince 6 years ago



      EE ..

    • profile image

      analyn 6 years ago

      thanks a lot

    • profile image

      Alexandria 6 years ago

      thank you very muchhhh xDD

    • profile image

      joyce 6 years ago

      grabe thanks po

      ang ganda wow

      my project n q kaso unti nga lang

    • profile image

      joyce 6 years ago

      thanks po

    • profile image

      janice j. vasquez 6 years ago

      2 too nga

    • profile image

      ruth=) 6 years ago

      thanks a lot....

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

    • profile image

      tine:)) 6 years ago

      thanks makakapasa na kmi:))

    • profile image

      vanessa jirah aparece 6 years ago

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

    • profile image

      gero gamarcha 6 years ago

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

    • profile image

      anne 6 years ago

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

    • profile image

      carsel 6 years ago


    • profile image

      jheiain yuri lee 6 years ago

      tnx for the explanation....

      nice one,..:P

    • profile image

      bryan 6 years ago

      thank u poh


    • profile image

      hazzel grace 6 years ago

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

    • profile image

      yancelyn 6 years ago

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

    • profile image

      rose 6 years ago

      thank very much

    • profile image

      jessie mendoza 6 years ago

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

    • profile image

      jimwellustares 6 years ago

      thank you for some informations in math

      i hope you will have more!!!!

    • profile image

      ella dapiton!!! 6 years ago

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

    • profile image

      chronous_03 6 years ago

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

    • profile image

      irish paola ave 6 years ago

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

    • profile image

      M.sailaja 6 years ago

      verrrrry simple nd sweet

    • profile image

      joanne 6 years ago

      yay! project finish!

    • profile image

      jhesa 6 years ago

      tnz po

    • profile image

      Angelo_4 6 years ago

      Like This

    • profile image

      maria 6 years ago


    • profile image

      margie 6 years ago

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

    • profile image

      danielle 6 years ago

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

    • profile image

      CHA 6 years ago

      yes nakita na jud ko sa answer


    • profile image

      sai 6 years ago

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

    • profile image

      rutine 6 years ago

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

    • profile image

      archiel 6 years ago

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

    • profile image

      lydia 6 years ago


    • profile image

      soniya 6 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

    • profile image

      jhAnexz 6 years ago

      yEhey ntpOx kOh nAh riN prOjeCt hehe :)

      i lOve iT!!!!

    • profile image

      donna 6 years ago

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

    • profile image

      donna ogayre 6 years ago

      i love mathematics... nice presentation

    • profile image

      Michael Coronejo 6 years ago

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

    • profile image

      loves 6 years ago


    • profile image

      mark joseph pili 6 years ago


    • profile image 6 years ago

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

    • profile image

      JOSEPH 6 years ago


    • profile image

      mhayla 6 years ago

      nakatulong po kau sa project namin salamt

    • profile image

      elina gilbert 6 years ago

      hahaha.. very simple....

    • profile image

      qwerty 6 years ago

      tenx poh

    • profile image

      jochelle matibag 6 years ago

      . thankz 4 that solution ..

      . mkakapasa na ako ng project nmin !

      thanz so much tlaga :)

    • profile image

      karl_18 6 years ago

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

    • profile image 6 years ago

      nice one it helps me very much!!!

    • profile image

      jessa mae realista 6 years ago

      thank you po

    • profile image

      frozen_fire 6 years ago

      can I post my problem too?.

    • profile image

      john alexis cruz 6 years ago

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

    • profile image

      angel 6 years ago

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

    • profile image

      michelle 6 years ago


    • profile image

      rhose 6 years ago

      great! a big help for me

    • profile image

      dwight 6 years ago

      thank you

    • profile image

      camille 6 years ago

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

    • profile image

      katrina 6 years ago

      nice, i have my assignment for tomorrow !:


    • profile image

      shenie bolina 6 years ago

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

    • profile image

      jacob 6 years ago

      thank' you are kind

    • profile image

      ann 6 years ago

      thanks a lot.. helpful talaga sya..

    • profile image

      Wouie Pajo 6 years ago

      Thanks for the answer.! GOD bless you!

    • profile image

      cath 7 years ago

      thank you. :)


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