Posted by tiffany on Thursday, August 27, 2009 at 10:52am.
Bill can mow his mothers lawn in 6 minutes. His brother Jim can mow it in 9 minutes. How long will it take them to do it together, if each has his own lawnmower? (record answer in minutes rounded to one decimal place. For example 14.2835 minutes, record 14.3).

Math  Reiny, Thursday, August 27, 2009 at 12:04pm
Bill's rate = lawn/6
Jim's reate = lawn/9
combined rate = lawn/6 + lawn/9
=5lawn/18
Time for combined effort = lawn/[5lawn/18]
= 18/5 minutes
= 3.6 minutes
Notice that "lawn" canceled, so we could have used any constant for "lawn"
in general for individual times of a,b,c,.. units of time
the time for a combined effort would be
1/[1/a + 1/b + 1/c + ...] units of time
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