The scale in a map is 1:22,000.000. Two cities are distant from New York 4 and 6cm, respectively. If a road was built connecting the three cities, what would the minimum extention of this road?

In my opinion, the minimun extension would be 6cm x 22million, which out result in 132,000.000 centimeters or 1320 kilometers. But the book says the correct answer would be 220km. Could anyone explain to me what did I do wrong? Cheers