Problema Solution
two pipes running simultaneously can fill a swimming pool in 6 hours. if both pipes run for 3 hours and one pipe is shut off, it takes 4 hours more for the remaining pipe to fill the pool. how long would it take for each pipe running separately to fill the pool?
Answer provided by our tutors
let
x = the time the first pipe needs to fill the swimming pool alone
y = the time the second pipe needs to fill the swimming pool alone
if the both pipes run 1 hour they will fill 1/6 of the pool
1/x + 1/y = 1/6
if the both pipes run for 3 hours and one is shut off it needs 4 hours more for the remaining pipe to fill the pool
3/x + 3/y + 4/y = 1
by solving the system of equations
1/x + 1/y = 1/6
3/x + 3/y + 4/y = 1
the positive solution
x = 24 hours
y = 8 hours
the first pipe alone needs 24 hours to fill the pool.
the second pipe alone needs 8 hours to fill the pool.