Problema Solution

Dave can dig a ditch in 6 hours, and Sam can dig a ditch in 4 hours. Frank can fill a ditch in 8 hours. If Dave and Sam dig a ditch while frank tries to fill it , how long does it take to dig the ditch altogether?

Answer provided by our tutors

Dave can dig a ditch in 6 hours thus his rate is 1/6 ditch per hour


Sam can dig a ditch in 4 hours thus his rate is 1/4 ditch per hour


Frank can fill a ditch in 8 hours thus his rate is 1/8 ditch per hour


let x = the hours they need to dig the ditch together thus the together rate is 1/x ditch per hour


1/6 + 1/4 - 1/8 = 1/x


by solving we find


x = 24/7 hr


x = 3 hr 3*60/7 min


x = 3 hr 26 min


x = 3.4 hr


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


Click to see all the steps



they will dig the ditch in 3.4 hours or 3 hours and 26 minutes approximately.