Columbus to Cincinnati

At 12:00 noon, Lunis started driving from Columbus to Cincinnati at a steady 40 mph. Fifteen minutes later, at 12:15, Ethan started driving from Cincinnati to Columbus at a steady 50 mph. The two cars passed each other at a point midway between the two cities. Using this information, calculate the distance between Columbus and Cincinnati. (Is this distance correct?)

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d r t L d/2 40 t E d/2 50 t – ¼

40t = 50(t – ¼) → 40t = 50t – 50/4
→ 50/4 = 50t – 40t → 12.5 = 10t
→ t = 1.25 hours (or 1 hour, 15 minutes)

So the distance each drove:

L = 40 x 1.25 = 50
E = 50 x 1 = 50

So according to the problem, Cincinnati and Columbus are 100 miles apart.

BUT according to the atlas, they’re really 109 miles apart. So how fast were Lunis and Ethan really going?