The Three Painters
17) It would take Jake 60 hours to paint his house. Dennis could
do it in 50; and Larry, in 53. If they all work together, how
long will it take?
1 1 1 1
--- + ---- + ---- = ----
60 50 53 x
Find the least common denominator:
56 = 2 * 2 * 2 * 7
60 = 2 * 2 * 3 * 5
50 = 2 * 5 * 5
-------------------------------
2 * 2 * 2 * 3 * 5 * 5 * 7 = 4,200
L.C.D. = 4,200x
4,200x (1) 4,200x (1) 4,200x (1) 4,200x (1)
----- + ---- + ---- = ------
60 50 56 x
x
4,200x / 60 = 70x
70x * 1 = 70x
4,200x / 50 = 84x
84x * 1 = 84x
4,200x / 56 = 75x
75x * 1 = 75x
4,200x / x = 4,200
4,200 * 1 = 4,200
70x + 84x +75x = 4,200
229x = 4,200
x = 18.34 hours, or 18 hours and 20 minutes