A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of the streetlight is 15 feet, what is the rate at which the person's shadow is lengthening?
(A) $1.5 \text{ ft/sec}$
(B) $2.667 \text{ ft/sec}$
(C) $3.75 \text{ ft/sec}$
(D) $6 \text{ ft/sec}$
(E) $10 \text{ ft/sec}$