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?

sandwich Aug 14, 2023

#1**+1 **

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

CPhill Aug 14, 2023