SOLUTION: Lynn and Farrah were asked to fill the tank with water. Lynn is twice faster than Farrah. Together, they filled it in two hours. How many hours can each of them alone fill the tank

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Question 1199453: Lynn and Farrah were asked to fill the tank with water. Lynn is twice faster than Farrah. Together, they filled it in two hours. How many hours can each of them alone fill the tank?
Found 4 solutions by josgarithmetic, math_tutor2020, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
                   RATE          TIME         TANKS

Lynn                               x           1

Farrah                            2x           1

Lynn_and_Farrah                   2            1







                           RATE          TIME         TANKS

Lynn                      1/x             x           1

Farrah                  1/(2x)           2x           1

Lynn_and_Farrah         1/2              2            1


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-------time for Lynn alone to fill the water tank;
Farrah alone needs 6 hours.
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Lynn works twice as fast compared to Farrah.
This means Lynn does 2/3 of the work when they team up.
Farrah does the remaining 1/3.
Note that 2/3 is twice that of 1/3; also the two fractions add to 1.

Consider a tank that is 24 gallons. You can pick any other multiple of 3.

Since Lynn does 2/3 of the work, she is able to fill (2/3)*24 = 16 gallons in 2 hours.
Her unit rate is 16/2 = 8 gallons per hour.
If Lynn worked alone, then she needs 24/8 = 3 hours to do the full job.

Relevant useful formulas
rate = (amount done)/(time)
time = (amount done)/(rate)

Farrah does 1/3 of the 24 gallons, so she fills (1/3)*24 = 8 gallons in 2 hours.
rate = 8/2 = 4 gallons per hour
If Farrah worked alone, then she would need 24/4 = 6 hours.
Or note that since Lynn takes 3 hours, Farrah would take 2*3 = 6 hours since Farrah works for twice as long.

----------------------------------------------------

Answers:
Lynn = 3 hours
Farrah = 6 hours
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

Lynn and  Farrah together work as productively as three instances of  Farrah,
and together they complete the job in  2  hours.

It means that  Farrah can complete the job in  2*3 = 6 hours  working alone.

It implies that  Lynn can complete the job in  6/2 = 3  hours working alone.


        *****************************************

                Four lines to complete the solution.
                Or  10  seconds to do it  MENTALLY.

        *****************************************


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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


My best comment on this problem is that a student should not be expected to spend any time working on the problem because of the exceedingly bad English used to present the problem.

I can GUESS what the statement "Lynn is twice faster than Farrah" means; but if I am being asked to solve a problem I should not have to guess what the given information means.

The other tutors who have responded all interpret the meaning of that statement to be that Lynn works twice as fast as Farrah -- i.e., can do the job in half the time that Farrah takes.

But one possible interpretation of the terrible English is that it takes Farrah THREE times as long as Lynn to do the job. That of course would lead to a different answer to the problem.

You could even make the argument that the statement that "Lynn is twice faster than Farrah" has nothing at all to do with how fast THEY DO THE WORK; it might mean that Lynn runs a 100-meter dash in half the time that Farrah does....
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