On their way Home / on the way home, they raped her.
Is there a synonym for 'on the way." I don't want to use an idiomatic expression, I have looked for possible synonyms but in vain.
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I don't know why the 0P doesn't want to use the phrase "on the way", which is so natural and commonly used. Nevertheless, the following are some alternatives he may like to use, depending on the context:
While they were going home.
While they were walking home.
While they were traveling home.
While they were driving home.
While they were heading home.
While they were making their way home.
On the way [to] X means while traveling [to] X - any word that means to travel can be substituted (i.e. while walking home, etc.)