Unformatted text preview: oe − river speed
= 6 miles − R miles
hour
hour
Proceeding as before, we get
5 miles = rate traveling upstream · time traveling upstream
5 miles = (6 − R) miles · time traveling upstream
hour
The last piece of information given to us is the total trip lasted 3 hours. If we let tdown denote the
time of the downstream trip and tup the time of the upstream trip, we have: tdown + tup = 3 hours.
Substituting tdown and tup into the ‘distanceratetime’ equations, we get (suppressing the units)
the following system of three equations and three unknowns: E 1 (6 + R) tdown = 5
E2
(6 − R) tup = 5 E3
tdown + tup = 3
We begin by solving E 1 for tdown by dividing both sides by the quantity (6 + R). While we usually
discourage dividing both sides of an equation by a variable expression, we know (6 + R) = 0 since
5
otherwise we couldn’t possibly multiply it by tdown and get 5. Hence, tdown = 6+R . Similarly, we
5
solve E 2 for tup and get tup = 6−R . Substituting these into E 3, we get:...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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