Math word problem help?

Jeff and Kirk can build a 75 ft wall together in 4 hours. Because Jeff has more experience, he could build the wall by himself 3 hours quicker than Kirk. How long would it take Kirk, (to the nearest minute) to build the wall by himself?



I know the answer is 9 hours and 46 minutes but I have no idea how they got it. Can someone help?



Answer on Math word problem help?



Jeff and Kirk can build a wall together in 4 hours

4[(1/J) + (1/K)] = 1



Jeff can build the wall by himself 3 hours quicker than Kirk

J = K - 3



4[(1/(K - 3)) + (1/K)] = 1

4[(K + K - 3) / (K(K - 3))] = 1

(8K - 12) / (K^2 - 3K) = 1

8K - 12 = K^2 - 3K

0 = K^2 - 11K + 12



solve quadratically

(11 ± v73) / 2

K ? {1.23, 9.77} hours



ignore the first answer because jeff would build the wall in negative time. doesn't make much sense

K does the job in 9.77 hours



9 hours and .77 * 60 minutes

9 hours and 46.2 minutes

to the nearest minute

9 hours and 46 minutes

Tweet