Question 880566
 Don williams uses his small motorboat to go 5 miles upstream to his favorite fishing spot.
 Against the current, the trip takes 5/12 hour.
 With the current the trip takes 1/4 hour.
 How fast can the boat travel in still water.
 What is the speed of the current.
:
let s = speed in still water
let c = rate of the current
then
(s-c) = effective speed up-stream
and
(s+c) = effective speed down-stream
:
Write a distance equation for each way; dist = time * speed
{{{5/12}}}(s-c) = 5
{{{1/4}}}(s+c) = 5
Get rid of those annoying fractions, mult the 1st eq by 12, the 2n by 4
5(s-c) = 60
s + c = 20
:
5s - 5c = 60
simplify, divide by5, add to the 2nd equation
s - c = 12
s + c = 20
--------------adding eliminates c, find s
2s = 32
s = 16 mph is the boat speed in still water
:
find the speed of the current
16 + c = 20
c = 20 - 16
c = 4 mph is the current
:
;
Check these solutions in the original equation
{{{5/12}}}(16-4) = 5
{{{5/12}}}*12 = 5
and
{{{1/4}}}(16+4) = 5
{{{1/4}}} * 20 = 5