college algebra

Question

a boat travels 3km upstream and 3km back. the time for the round trip is 8 hours. the speed. the speed of the stream is 3km/hr. what is the speed of the boat in still water?
simplify your answer, type as an interger or fraction, round to the nearest hundredth

 

Answer 1

When the boat is traveling upstream, it's speed is v - 3, and similarly for downstream its v + 3, where v is the speed of the boat relative to the water. 

The time to go upstream is 3/(v-3) and to go downstream its 3/(v+3). With total time = 8, we have 

3/(v-3) + 3/(v+3) = 8.

3(v+3) + 3(v-3) = 8(v² - 9)

6v = 8v² - 72

8v² - 6v - 72 = 0

Applying the quadratic formula and ignoring the negative solution gives v = 3.40 km/hr.  

Answer 2

Here is another way: solving the upstream time first.

Let t = upstream time. Thus, 8-t is downstream time.

Since the difference between the upstream speed and downstream speed is 6 km/h, we have

3/t - 3/(8-t) = 6

Solve for t,

(8-t) - t = 2t(8-t)

2t^2 - 18t + 8 = 0

t^2 - 9t + (9/2)^2 = 49

(t-3/2)^2 = 49

t = 1.5+7 = 8.5 hrs

For upstream, (v-3)t = 3

Solve for v, v = 3.35 km/hr <==Answer