See the attached image.

Denote the common time as `T ` and the equidistant point as `A`. Each woman is under the influence of the current, so they have to direct to point `B`, `14T ` to the west of `A`. In the coordinate system connected with flowing water, they make `60T ` and `80T`, respectively.

We can write two equations using the Pythagorean theorem:

`sqrt( ( 60T )^2 - W^2 ) + 14T = D/2`, `sqrt( ( 80T )^2 - W^2 ) - 14T = D/2`, where `W ` means the river width. They are equivalent to `( 60T )^2 - W^2 = (D/2)^2 + (14T)^2 - 14TD`, `( 80T )^2 - W^2 = (D/2)^2 + (14T)^2 + 14TD`.

Add the two equations and obtain `( (60)^2 + (80)^2 - 2*(14)^2 ) T^2 - 2W^2 = D^2/2`.

Subtract them and obtain `((80)^2-(60)^2)T^2 = 28TD`, or `(40^2-30^2)T = 7D`, or `T = D/100`. Substitute this into the sum of equations:

`D^2 / 100^2 ((60)^2 + (80)^2 - 2*(14)^2 - 5000) = 2W^2`, or `D^2 = 100^2/48^2 W^2`, so `D = 100/48 W = 100*5.5 = 550 ` (meters), which is the answer.

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