Problema Solution
Two pipes, A and B, are used to fill a water tank. The empty tank is filled in 10 hours if the two pipes are used together. If pipe A alon e is used for 6 hours and then turned off, pipe B will take over and finish filling the tank in 18 hours. How long will it take each pipe alone to fill the tank?
Answer provided by our tutors
let
a = the hours the pipe A need to fill the tank alone
b = the hours the pipe B need to fill the tank alone
the empty tank is filled in 10 hours if the two pipes are used together
1/a + 1/b = 1/10
1/a = 1/10 - 1/b
if pipe A alone is used for 6 hours and then turned off, pipe B will take over and finish filling the tank in 18 hours
6/a + 18/b = 1
plug 1/a = 1/10 - 1/b into the last equation
6(1/10 - 1/b) + 18/b = 1
by solving we find
b = 30 hr
click here to see the step by step solution of the system of equations
1/a = 1/10 - 1/30
a = 15 hr
click here to see the step by step calculation for a
pipe A will fill the pool alone is 15 hours.
pipe B will fill the pool alone in 30 hours.