Question 170286
Let v = speed of paddleboat w/no current
.
Applying "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
Let t = time traveling upriver
then
2-t = time traveling downstream
.
We have two unknowns (v and t) so we'll need two equations:
t(v-4) = 1 (equation 1)
(2-t)(v+5) = 1 (equation 2)
.
Solving equation 1 for 't':
t(v-4) = 1
t = 1/(v-4)
.
Substitute the above into equation 2 and solve for v:
(2-(1/(v-4)))(v+5) = 1
multiply both sides by (v-4):
(2(v-4) - 1)(v+5) = 1
(2v-8 - 1)(v+5) = 1
(2v-9)(v+5) = 1
Applying FOIL:
2v^2 + 10v - 9v -45 = 1
2v^2 + v -45 = 1
2v^2 + v -46 = 0
.
Can't factor so use the quadratic formula.  Doing so will yield:
v = {4.552, -5.052}
.
We can toss out the negative solution leaving us with:
v = 4.552 km/hr
.
Details of quadratic below:
*[invoke quadratic "v", 2, 1, -46 ]