Ben's Son
20) Ben can rake the backyard in 45 minutes. With his son's
help, they can finish the job in 20 minutes. How long would it
take Ben's son to rake all the backyard by himself?
Here's a way of looking at this:
People Length of Time Part of Job Done
Involved to Do the Job in 1 Minute
-------- ------------- ----------------
Ben 45 1/45
Ben's son x 1/x
Together 20 1/20
1 1 1
--- + ----- = -----
45 x 20
Find the Lowest Common Denominator:
45 = 3 * 3 * 5
20 = 2 * 2 * 5
-----------------------
2 * 2 * 3 * 3 * 5 = 180
L.C.D. = 180x
180x (1) 180x (1) 180x (1)
---- + ---- = -----
45 x 20
180x / 45 = 4x
4x * 1 = 4x
180x / x = 180
180 * 1 = 180
180x / 20 = 9x
9x * 1 = 9x
4x + 180 = 9x
180 = 5x
x = 36 (minutes for the son to rake the entire backyard by
himself)