<PRE><B>Question 1174768</B>
Jeff and Kirk can build a​ 75-ft retaining wall together in 4 hours.
 Because Jeff has more​ experience, he could build the wall by himself 2 hours quicker than Kirk.
How long would it take Kirk​ (to the nearest​ minute) to build the wall by​ himself?
:
the length of the wall is not relevant in this problem
:
let t = time required by Kirk to build the wall by himself
Jeff takes 2 hrs less, therefore
(t-2) = time required by Jeff
let the completed job = 1
:
{{{4/t}}} + {{{4/((t-2))}}} = 1
multiply eq by t(t-2), cancel the denominators
4(t-2) + 4t = t(t-2)
4t - 8 + 4t = t^2 - 2t
8t - 8 = t^2 - 2t
arrange as a quadratic equation on the right
0 = t^2 - 2t - 8t + 8
0 = t^2 - 10t + 8
using the quadratic formula, a=1; b=-10, c=8, the positive solution
t = 9.1231 hrs
which is 9 + .1231(60) 9 hrs 7 min is time required by Kirk alone</PRE>