You got the first equation right, in expressing time-taken in terms of b and w.

Now you need the second equation, which expresses b in terms of w (or vice-versa). Hard to describe it here over text, but I believe using the following set of equations, it should be possible to express b in terms of w.

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Yb = vertical-distance from start-point to water (constant)

Yw = vertical-distance from water to end-point (constant)

Xb = horizontal-distance between start and point-of-contact with water

Xw = horizontal-distance between end and point-of-contact with water

X = horizontal-distance between start/end points (constant)

Ob = angle taken when running towards the water

Ow = angle taken when swimming towards the end point

=>

X = Xb + Xw

cos(Ob) = Yb / b

sin(Ob) = Xb / b

cos(Ow) = Yw / w

sin(Ow) = Xw / w