While on vacation, Kevin went for à swim in a nearby lake. Swimming against the current, it took him 8 minutes to swim 200 meters. Swimming back with the current took half as long. What is his and the lake's current average speed?

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Answer 1 · 2017-12-01T09:40:15

Kevin's speed is 37.5 meters per minute. Lake's current has a speed of 12.5 meters per minute.

You have two equations and two unknowns.

Let me assign k as Kevin's speed and c as the speed of current.

#k-c = 25# because it takes 8 minutes to swim 200 meters against the current (#200/8=25 # meters per minute).

#k+c = 50# because it takes 4 minutes to swim 200 meters when he swims on the same directions of the current (#200/4 = 50# meters per minute).

When you add these two equations:

#k-c + k+c = 25+50#

#2timesk = 75# and

#k=37.5# meters per minute.

Put this value into any equation provided abobe

#k-c = 25#

#37.5-c = 25#

#37.5 - 25 = c = 12.5# meters per minute.

Kevin's speed (in water) is 37.5 meters per minute and current speed is 12.5 meters per minute.