SOLUTION: Karla cleaned her garden by raking.she took 40 min to finish. mike took 60 min for the same place to clean.if karla started 10 minutes before,How much time will take to fish clean

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Karla cleaned her garden by raking.she took 40 min to finish. mike took 60 min for the same place to clean.if karla started 10 minutes before,How much time will take to fish clean      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 615963: Karla cleaned her garden by raking.she took 40 min to finish.
mike took 60 min for the same place to clean.if karla started 10 minutes before,How much time will take to fish cleaning together?
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of cleaning to get their rate working together
Karla's rate: ( 1 garden cleaned ) / ( 40 min )
Mike's rate: ( 1 garden cleaned ) / ( 60 min )
---------
What fraction of the job did Karla get done in 10 min?
+%281%2F40%29%2A10+=+1%2F4+
So, 1/4 of the garden is cleaned before they both start working together
That means 3/4 of the garden is left to clean
Let +t+ = the time in minutes for them to finish working together
+1%2F40+%2B+1%2F60+=+%283%2F4%29+%2F+t+
+1%2F40+%2B+1%2F60+=+3%2F%284t%29+
Multiply both sides by +120t+
+3t+%2B+2t+=+90+
+5t+=+90+
+t+=+18+
it takes them 18 minutes to finish together
check:
+1%2F40+%2B+1%2F60+=+3%2F%284t%29+
+1%2F40+%2B+1%2F60+=+3%2F72+
+1%2F40+%2B+1%2F60+=+1%2F24+
+1%2F10+%2B+1%2F15+=+1%2F6+
+60%2F10+%2B+60%2F15+=+60%2F6+
+6+%2B+4+=+10+
+10+=+10+
OK

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Karla cleaned her garden by raking.she took 40 min to finish.
mike took 60 min for the same place to clean.if karla started 10 minutes before,How much time will take to finish cleaning together?
Let x = the answer.  Make this chart and put x for the time Karla and Mike
rake together.

                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden
Mike alone raking 1 garden
Karla raking alone 10 minutes 
Karla and Mike raking together                             x

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

Karla takes 40 minutes to rake 1 garden so put 40 for her time and 1 for
the number of gardens she rakes in 40 minutes.

                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden                 1             40         
Mike alone raking 1 garden                   
Karla raking alone 10 minutes 
Karla and Mike raking together                             x

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

Mike takes 60 minutes to rake 1 garden so put 60 for his time and 1 for
the number of gardens he rakes in 60 minutes

                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden                 1             40
Mike alone raking 1 garden                  1             60 
Karla raking alone 10 minutes 
Karla and Mike raking together                             x

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

Fill in their rates in gardens/minute by dividing the number of gardens
by the number of minutes:


                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden                 1             40         1/40
Mike alone raking 1 garden                  1             60         1/60
Karla raking alone 10 minutes 
Karla and Mike raking together                             x

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

Karla's rate for the 10 minutes she worked alone is the same as when she
rakes 1 whole garden so fill in 1/40 for her rate there too, and 10 for the
number of minutes:


                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden                 1             40         1/40
Mike alone raking 1 garden                  1             60         1/60
Karla raking alone 10 minutes                             10         1/40
Karla and Mike raking together                             x

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

Find the fraction of a garden Karla raked in those 10 minutes by multiplying
her rate in gardens/min by the number of min: 10(1/40) = 1/4. Fill that in: 


                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden                 1             40         1/40
Mike alone raking 1 garden                  1             60         1/60
Karla raking alone 10 minutes              1/4            10         1/40
Karla and Mike raking together                             x

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

Find their combined raking rate by adding their rates:
1/40 + 1/60 = 3/120 + 2/120 = 5/120 = 5/120 = 1/24. Fill that in: 


                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden                 1             40         1/40
Mike alone raking 1 garden                  1             60         1/60
Karla raking alone 10 minutes              1/4            10         1/40
Karla and Mike raking together                             x         1/24

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

Find the fraction of a garden they raked together by multiplying their
combined rate 1/24 by the number of minutes x, getting x/24.  Fill that
in:



                                        Number of        Time      Raking       
                                      gardens raked     raked        Rate 
                                      or fraction         in          in
                                        thereof        minutes    gardens/min
Karla alone raking 1 garden                 1             40         1/40
Mike alone raking 1 garden                  1             60         1/60
Karla raking alone 10 minutes              1/4            10         1/40
Karla and Mike raking together            x/24             x         1/24

The equation comes from:

        +  = %28matrix%282%2C1%2C++%0D%0A%0D%0Aone%2C+garden%29%29 


       1%2F4 + x%2F24 = 1

Multiply both sides by 24

       6 + x = 24
           x = 18

It took the 18 minutes to finish.

Edwin