The tickets for our journey from Northampton to Frome are

split three ways and I have calculated the relative costs per mile of each leg. The results are interesting, see...

Northampton to Birmingham stations - advanced single - 7pence/mile
Birmingham stations to Worcestershire Parkway - off-peak return - 43pence/mile
Worcestershire Parkway to Frome - off-peak return - 6pence/mile

Please note that the above costs include our two together discounts loaded at about thirty-three per cent.