Sam is swimming at a rate of 450 ft in 4 minutes means:

d = 450 ft the distance

t = 4 min the time

v = the average rate

v = 450/4 (since rate = distance/time)

v = 112.5 ft/min

Sam's rate is 112.5 ft/min.

Now we have, t = 15 min and v = 112.5 ft/min, we need to find the distance d.

v = d/t

d = v*t

d = 112.5*15

d = 1,687.5 ft

In 15 minutes time Sam will swim a distance of 1,687.5 feet.