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.