Jeff and Kirk Math Problem

Question

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?

Answer 1

Let J = Jeff's time alone and K = Kirk's time alone

J = K -2

(1/J) + (1/K) = 1/6

[1/(K-2)} + (1/K) = 1/6

When you clear fractions and collect terms, you get

K²-14K + 12=0 which (by quadratic formula) has only 1 root which makes sense for this problem, namely

K=13.08 and J=11.08

Now why??? The "job" is 75', but the value is not essential to the problem.

1/J and 1/K and 1/6 are rates...job per unit time

The time to do the job cancels out:

T(1/J) + T(1/K) = T/6.

I always have trouble explaining work problems, BUT this is the way to solve them, at least every time I have seen one this method works!