Mary swam 2 kilometers against the current in the same amount of time it took her to swim 8 kilometers with the current. the rate of the current was 3 kilometers per hour. how fast would mary swim if there were no current?

Let the speed of Mary with no current be x km/h

speed of current = 3 km/h

Time=distance/speed

distance swum against current=2km

Time taken to swim against current=2 / (x-3)

distance swum with current=8km

Time taken to swim with current=8 / (x+3)

Given that the time taken in both instances are the same, then:

2 / (x-3) = 8 / (x+3)

solving for x we get:

2 (x+3) = 8 (x-3)

2x+6=8x-24

6+24=8x-2x

30=6x

x=30/6=5 km per hour

Therefore we conclude that:

Mary's speed with no current is 5 km/h