Analyzing Rational Functions

Question

Lenny Leonardson can paddle in still water at a speed of 4km/h. If he paddled 8km upstream against the current and then paddled 8km back downstream with the current and the total trip took 5h, what is the speed of the current?

the answer is 1.79km/h

Answer 1

Let c = the speed of the current and t be time. Remember d = rt or r = d/t

Rate upstream is 4-c and downstream 4+c

The two equations are derived from both r=d/t:

4-c = 8/t

4+c = 8/(5-t)

Add the two equations

8 = 8/t + 8/(5-t) --> 8= 40/(t(t-5)) --> t = (5 + √5)/2 by picking the positive one

Substitute that into 4-c = 8/t --> c = 8/((5 + √5)/2) - 4 --> c = (4/5)√5

Answer 2

t_down + t_up = 5

t_down = 8 / (4 + c)

t_up = 8 / (4 - c)

[8 / (4 + c)] + [8 / (4 - c)] = 5

Can you solve for c and answer?