Distance, Rate, and Time w/ current

Question

Brian decides to start training for swimming in a river. The current in the river is
4km/hr. If he swims upstream 2 km and then back downstream to where he started in 3
hours, what is his swimming speed?

Answer 1

Let x = swimming speed if there is no current

 

Swimming speed upstream = x-4

 

Swimming speed downstream = x+4

 

Distance = (Rate)(Time), so Time = (Distance)/(Rate)

 

Time upstream + Time Downstream = 3

 

So, 2/(x-4) + 2/(x+4) = 3

 

2(x+4) + 2(x-4) = 3(x+4)(x-4)

 

                     4x = 3x² - 48

 

       3x² - 4x - 48 = 0

 

       x = [4 ± √592]/6 ≈ 4.72 or -3.39

 

Since x can't be negative, x ≈ 4.72 km/hr