A kayak can travel 72 miles downstream in 8 hours, while it would take 24 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current?

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Answer 1 · 2018-02-23T09:02:08

Speed of kayak #k=6# mph and speed of river (current) #r=3# mph

mph stands for miles per hour (speed).

Your equations (the same direction when kayak and the river travels):

#k+r = 72/8#

#k+r = 9# miles per hour

On the other hand (the opposite directions, kayak is faster than the current)

#k-r = 72/24#

#k-r = 3#

Now you have two equations:

#k+r = 9#
#k-r = 3#

Combine these two and it is gotten:
#2k = 12#

#k=6# miles per hour.

Since #k-r=3#
r will be 3 miles per hour.

A kayak can travel 72 miles downstream in 8 ​hours, while it would take 24 hours to make the same trip upstream. Find the speed of the kayak in still​ water, as well as the speed of the current?