Unexpected error when implementing FEM in MoL SpatialDiscretization

I cannot figure out why the following piece of code

PDEs = {Derivative[1, 0][w][t, x] == w[t, x]/v[t, x],
Derivative[1, 0][v][t, x] == 0};

IC = {w[0, x] == 0, v[0, x] == 1};

BC = {w[t, 1] == 0, v[t, 1] == 1};

AbsoluteTiming[
evolution =
NDSolve[{PDEs, IC, BC}, {w, v}, {t, 0, 1}, {x, 0, 1},
Method -> {"MethodOfLines",
"SpatialDiscretization" -> {"FiniteElement",
"MeshOptions" -> MaxCellMeasure -> 0.01}}];]


results in

NDSolve::femcnsd: The PDE coefficient w[x]/v[x] does not evaluate to a numeric scalar at the coordinate {0.5}; it evaluated to Indeterminate instead.

instead of the profound result $$w(t,x)=v(t,x)-1=0$$.

Can anyone help?

PS: Replace w[t, x]/v[t, x] with w[t, x]*v[t, x] in the code, i.e.

 PDEs = {Derivative[1, 0][w][t, x] == w[t, x]*v[t, x],
Derivative[1, 0][v][t, x] == 0};

IC = {w[0, x] == 0, v[0, x] == 1};

BC = {w[t, 1] == 0, v[t, 1] == 1};


and it works just fine. It seems that my code understands * but not /.

In some rare cases of coupled DEs, NDSolve can not automatically figure out the ordering of the equations. This works:

PDEs = {Derivative[1, 0][w][t, x] == w[t, x]/v[t, x],
Derivative[1, 0][v][t, x] == 0};
IC = {w[0, x] == 0, v[0, x] == 1};
BC = {w[t, 1] == 0, v[t, 1] == 1};
AbsoluteTiming[
evolution = NDSolveValue[{PDEs, IC, BC}, {w, v}, {t, 0, 1}, {x, 0, 1},
"DependentVariables" -> {w, v},
Method -> {"MethodOfLines",
"SpatialDiscretization" -> {"FiniteElement",
"MeshOptions" -> MaxCellMeasure -> 0.01}}];]


Check the result:

Plot3D[#[t, x], {t, 0, 1}, {x, 0, 1}] & /@ evolution


You can find more information on this issue in the documentation here.