+1348 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?
+129771 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
