Jeff and Kirk can build a 75-ft retaining wall together in 6 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?
1 wall/ (1 wall/ j+ 1 wall/ k) = 6 where j and k are the times for each Jeff and Kirk
1 wall/ (j) = 1 wall/(k -2) sub this into the first equation above
1 / (( 1/(k -2) + 1/k ) = 6
1 / k-2 +k / (k^2 - 2k)
(k^2-2k) / (2k-2) = 6
k^2 -2k = 12k - 12
k^2 -14k + 12 = 0 k = 13.0828 or .91724 hrs (throw out)
k=13.0828 hrs then j = 11.0828 hrs
check 1 / (1/11.0828 + 1/13.0828) = 6 ?
6 = 6 Check !
Kirk by himself = 13.0828 hrs = ~~13 hrs 5 mins