A kayak can travel 24 miles downstream in 3 ​hours, while it would take 12 hours to make the same trip upstream. Find the speed of the kayak in still​ water, as well as the speed of the current?

1 Answer
Dec 1, 2017

Kayak: #5mph#

Current: #3mph#

Explanation:

The equation you need to know is #d=rt#. However, there are two things moving: the kayak and the current. Let #k# be the speed of the kayak in still water and #c# be the speed of the current.

When traveling downstream, the two speeds add. That is:

#d=(k+c)t_(down)#

#24=3(k+c)#

#8=k+c#

When traveling upstream, however, the current opposes the kayak speed so it subtracts.

#d=(k-c)t_(up)#

#24=12(k-c)#

#2=k-c#

Now, we can add the two equations to get:

#8+2=(k+c)+(k-c)#

#10=2k#

#k=5#

So, the kayak travels #5 mph#. We can plug this back into one of our other equations to get #c=3#. So, the speed of the current is #3mph#.