If one shortens prayer for travel during Ramadan, must they also not fast?

Someone travelling during Ramadan does not have to fast that day (but catch it up later); Qur'an 2:184 . Someone travelling can also shorten their prayer; Qur'an 4:101 . **Question**: If one shortens prayer for travel during Ramadan, must they also not fast? It seems inconsistent to shorten the prayer due to travel, yet not break the fast due to travel. But maybe I'm reading too much into this, and flexibility is intended. ---- To reiterate, this is the scenario: 1. We have someone who is travelling during Ramadan. 2. They don't have to fast that day due to travelling, but choose to fast anyway. 3. They shorten prayer that day due to travelling. It seems inconsistent, and I'm wondering if this is not allowed.