Related Rates: inverted cone

A cone (pointing downward) has a depth of 8m and a radius of 5m. Beginning at t=0, two things start happening: the radius begins expanding at 1 meter/sec, and water is poured in at a rate of 3 cubic meters/sec. The depth of the cone stays constant.

At what time does the depth of the water reach a maximum?

I've got an answer that I feel good about, but I'd like a more elegant method. Specifically, it'd be nice to know if this is possible without rewriting each part as a function in terms of time.

My answer in white text: t = 5.