This should give you a nudge in the direction.
This code needs to placed in functions.php.
function acf_57448( $post_id ) {
$start_date = get_field( 'field_name', $post_id );
// do stuff to calculate ETA
update_field( 'eta_field_name', $post_id )
}
add_action( 'acf/save_post', 'acf_57448', 20 );