Unformatted text preview: so let’s call this quantity R, with units
garden
hour . Using the fact that rates are additive, we have:
rate working together = rate of Taylor working + rate of Carl working
1 garden
3 hour so that R = 1 garden
12 hour . = 1 garden
4 hour + R garden
hour Substituting this into our ‘workratetime’ equation for Carl, we get:
1 garden = (rate of Carl working) · (t hours)
1 garden = Solving 1 = 1
12 t, 1 garden
12 hour · (t hours) we get t = 12, so it takes Carl 12 hours to weed the garden on his own.5 Even though a system of equations wasn’t formally used in Example 8.7.4, the notion of using two
variables and two unknowns is there, albeit it more subtly than in Example 8.7.3. As is common
with ‘word problems’ like Examples 8.7.3 and 8.7.4, there is no ‘shortcut’ to the answer. We
encourage the reader to carefully think through and apply the basic principles of rate to each
(potentially diﬀerent!) situation. It is time well spent. We also encourage keeping track of units,
especially in th...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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