Sam and Dave
16) If Sam can rake the leaves in the front yard in 35 minutes,
and Dave can do the same job in 40 minutes, then how long would
it take if they work together?
1 1 1
--- + ----- = ---
35 40 x
Find the least common denominator:
35 = 5 * 7
40 = 2 * 2 * 2 * 5
-----------------
2 * 2 * 2 * 5 * 7 = 280
L.C.D. = 280x
280x (1) 280x (1) 280x (1)
--- + ---- = ---
35 40 x
280x/35 = 8x
8x * 1 = 8x
280x/40 = 7x
7x*1 = 7x
280x/x = 280
280 * 1 = 280
8x + 7x = 280
15x = 280
x = 18.66 minutes, or 18 minutes and 40 seconds.