Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $25$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}15$ p.m. If they always row directly towards each other, and the lake is $4500$ meters across from the west side of the lake to the east side, at what time will the two meet?