Question 1039010
<font face="Times New Roman" size="+2">


Let the rate of the steamboat be represented by *[tex \Large r] and the rate of the current be represented by *[tex \Large r_c].  Since the trip from A to B takes less time than from B to A, the boat must be going with the current.  That means that the total speed of the boat with respect to the bank of the river is *[tex \Large r\ +\ r_c].  Likewise, going back upstream, the speed is *[tex \Large r\ -\ r_c].


Let *[tex \Large d] represent the distance from A to B.  One assumes that A and B are fixed points so that the distance remains constant regardless of the direction of travel.  We know that distance equals rate times time, so the downstream trip is modeled by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 5(r\ +\ r_c)]


and the upstream trip by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 7(r\ -\ r_c)]


Since *[tex \Large d\ =\ d], we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7(r\ -\ r_c)\ =\ 5(r\ +\ r_c)]


Solving:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r\ =\ 6r_c]


And substituting into the model for the downstream trip:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 5(6r_c\ +\ r_c)\ =\ 5(7r_c)\ =\ 35r_c]


Dividing both sides by *[tex \Large r_c] we get:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{r_c}\ =\ 35]


And since time is equal to distance divided by rate, we have our answer.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>