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