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# help plz

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Help I'm confused with rates

Two hoses, A and B, are used to fill a fish tank with water.  Hose A puts water into the tank three times as fast as hose B.  If both hoses are used, the tank is filled four minutes faster than if just hose A is used.  How many minutes would it take for hose B to fill the tank on its own?

Aug 14, 2023

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Let  A's rate per minute  =  3/R =  the amt of the job that A can do in one minute

Let B's rate per minute = 1/R = the amt of the  job that B can  do in one  minute

And rate * time = part of job done       (a whole job done = 1)

So  with A alone let the time = T    and we  have

(3/R) * (T ) =  1

3T  = R

T = R/3

With both hoses operating  let the time = T - 4  and we  have

(3/R) * (T - 4)  + (1/R) *  ( T - 4)  =   1

3 ( R/3 - 4) / R  +  (R/3 - 4) /R  =  1               multiply through by R

R - 12 + R/3 - 4  =  R    rearrange as

R + R/3 - R =  16

R/3 =  16

R = 48

B's  rate per minute =  1/R = 1/ 48 of the job done.....so it takes  B 48 minutes to fill the tank alone   Aug 14, 2023