the pipe that can fill the pool in 5 hours has a rate of 1/5 pool per hour

the pipe that can fill the pool in 8 hours has a rate of 1/8 pool per hour

let x = the hours that the both pipes will need to fill a pool together, x>0

the together rate is 1/x pool per hour

1/5 + 1/8 = 1/x

by solving we find:

x = 40/13

x = 3 hr (1/13)*60 min

x = 3 hr 4.6 min

click here to see the step by step solution of the equation:

using both pipes it will take around 3 hours and 5 minutes to fill the pool.