Question

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?

Answer 1

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`.