let

c = 3 mph the speed of the current in a creek

v = the speed of swans kayak in still water

t = the time of the kayaking in each direction

d1 = 4 mi the distance of the upstream kayaking

d2 = 10 min the distance of the downstream kayaking

since distance = speed*time we have:

kayaking upstream the speed of the kayak is v - c and

(v - c)t = d1

(v - 3)t = 4

t = 4/(v - 3)

kayaking downstream the speed of the kayak is v + c and

(v + c)t = d2

(v + 3)t = 10

plug t = 4/(v - 3) into the last equation:

(v + 3)(4/(v - 3)) = 10

by solving we find:

v = 7 mph

click here to see the step by step solution of the equation:

the speed of swans kayak in still water is 7 mph.