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Unformatted text preview: is encouraged to check the units in this equation are the same on both sides. To get you started, the
units on the ‘3’ is ‘hours.’ 540 Systems of Equations and Matrices amount of work Taylor does = rate of Taylor working · time Taylor spent working
1 garden = (rate of Taylor working) · (4 hours)
So we have that the rate Taylor works is 14garden = 1 garden . We are also told that when working
together, Taylor and Carl can weed the garden in just 3 hours. We have:
amount of work done together = rate of working together · time spent working together
1 garden = (rate of working together) · (3 hours)
From this, we ﬁnd the rate of Taylor and Carl working together is 13garden = 1 garden . We are asked
to ﬁnd out how long it would take for Carl to weed the garden on his own. Let us call this unknown
t, measured in hours (to be consistent with the other times given to us in the problem.) Then:
amount of work Carl does = rate of Carl working · time Carl spent working
1 garden = (rate of Carl working) · (t hours)
In order to ﬁnd t, we need to ﬁnd the rate of Carl working,...
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