Word math problem

Question

The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. If the ship uses 250 barrels of oil in traveling 500 miles at 48 mph, determine how many barrels of oil are used when the ship travels 480 miles at 24 mph.

Answer 1

Let b = barrels if oil, s = speed, d = distance

b = kds²

when b = 250, d = 500 and s = 48

250 = k(500)48²

k = 1/(2(48)²)

when d = 480 and s = 24

b = (1/(2(48)²))480(24)² = (480/2)(24/48)² = 240(1/4) = 60 barrels