Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How long would it take each of them to do the job alone?
+23246 Let 1/d be the rate that Dwight works [1 job every d hours]
Then 1/(d - 3) is the rate that Joe works [1 jobe every d - 3 hours]
rate x time = amount done Total amount done is 1 job
(amount done by Dwight) + (amount done by Joe) = Total work done
(1/d) x 2 + ( 1/(d - 3) } x 2 = 1
Mulriply both sides by d · (d - 3):
[d · (d - 3)] · (1/d) x 2 + [d · (d - 3)] · ( 1/(d - 3) ) x 2 = 1 · [d · (d - 3)]
2(d - 3) + 2d = d2 - 3d
2d - 6 + 2d = d2 - 3d
0 = d2 - 7d + 6
0 = (d - 6)(d - 1)
If d = 6 hours (Dwight), then d - 3 = 3 hours (Joe).
