A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. How do you find the speed the kayaker would make in still water?

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Answer 1 · 2018-08-05T02:55:32

# 6/5 mph#

D = RT
As the Distance is the same

# R_1 xx T_1 = R_2 xx T_2 #

Let K equal the rate of the Kayaker in still water

# ( 6 + K) xx 2 = ( 6 -K ) xx 3 #

Multiplying across the parenthesis gives

# 12 + 2K = 18 - 3K #

Adding the opposite to both sides of the equation gives

# 12 - 12 + 2K + 3K = 18 - 12 - 3K + 3K#

The result is

# 5K = 6 #

Dividing both sides by 5

# 5K/5 = 6/5 #

# K = 6/5 #