Question

David swam 8 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 1 kilometer per hour. How fast would David swim if there were no current?

Answer 1

David can swim at a speed of 3 kilometers per hour in still water, as determined by setting up equations for the rate of swimming against and with the current, and solving for the unknown speed.

Step-by-step explanation:

David swam 8 kilometers against the current and 16 kilometers with the current in the same amount of time. To find how fast David can swim in still water, we can set up two equations based on the fact that distance equals rate multiplied by time (D = RT), and solve for David's swimming speed in still water. Let's denote David's speed in still water as 's' and the rate of the current as 'c' which is given as 1 kilometer per hour.

Swimming against the current, his effective speed would be (s - c), and with the current it would be (s + c). Since the time to swim each distance is the same, we have the equations:

• 8/(s - 1) = 16/(s + 1)

Multiplying both sides by (s - 1)(s + 1) to clear the denominators, we get:

8(s + 1) = 16(s - 1)

Solving for 's', we will get David's speed in still water:

8s + 8 = 16s - 16

8s - 16s = -8 - 16

-8s = -24

s = 3 kilometers per hour

Therefore, David's speed in still water is 3 kilometers per hour.