A kayak can travel 60 miles downstream in 10 hours while it would take 30 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current. Let k represent the speed of the kayak in still water and let c represent the speed of the current.
we have
k -------> represents the speed of the kayak in still water
c -----> represents the speed of the current
so
downstream
Remember that
the speed is equal to divide the distance by the time
s=d/t
d=s*t
60=(k+c)*10
k+c=6 ------k=6-c -----> equation 1
upstream
60=(k-c)*30
k-c=2 ------> k=2+c -----> equation 2
equate equation 1 and equation 2
6-c=2+c
solve by c
2c=6-2
2c=4
c=2
Find the value of k
k=6-2 -----> k=4
therefore
the speed of the kayak in still water is 4 mph
the speed of the current is 2 mph