How fast would Austin swim with no current

Question

Austin swam 4 kilometers against the current in the same amount of time it took him to swim 16 kilometers with the current. The rate of the current was 3 kilometers per hour. How fast would Austin swim if there were no current?

Answer 1

Distance = Rate x Time

 

Let Austin's swimming speed = X

 

4 km =   (X-3) * Time

 

16 km = (X+3) * Time

 

Solving both equations for Time and setting them equal:

 

4/x-3 = 16/x+3

 

Cross Multiply:  4(x+3) = 16(x-3)

                      4x + 12 = 16x - 48  <-- distributive

                    0 = 16x - 48 - 4x - 12  <-- everything to the right side

                   0  = 12x - 60   <--- combines like terms

                   60 = 12x   <-- adds 60 to both sides

                     x= 5 <-- divides bot sides by 12

 

Austin swims 5 km/hour

 

With the current he swims 8 km/hour in 2 hours.

Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.