A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
a)15:46
b)3:10
c)12:23
d)5:18
e)10:3
Let the task = the LCM of 1, 3, 4 and 6 = 12 widgets.
Since the husband takes 1 hour to complete the task, the husband's rate = w/t = 12/1 = 12 widgets per hour.
Since the wife takes 2 hours to complete the task, the wife's rate = w/t = 12/2 = 6 widgets per hour.
Combined rate for the husband and wife = 12+6 = 18 widgets per hour.
Since Rae takes 4 hours to complete the task, Rae's rate = w/t = 12/4 = 3 widgets per hour.
Since Herman takes 6 hours to complete the task, Herman's rate = w/t = 12/6 = 2 widgets per hour.
Combined rate for Rae and Herman = 3+2 = 5 widgets per hour.
Rate and time have a RECIPROCAL RELATIONSHIP:
3 times as fast implies 1/3 the time.
1/2 the time implies twice the rate.
The RATE RATIO for the adults and children = (18 widgets per hour) : (5 widgets per hour).
Thus, the TIME RATIO is equal to the reciprocal:
(5 hours) : (18 hours).
The correct answer is
D.
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