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Let's say we have the first toll at distance 0 ,
the next toll at distance greater than 10 ( 10.1 ) ,
the next toll at distance greater than 10 of the last one ( 20.2)
....since the last one is at distance 25 from the first one...the distance from the third and fourth has to be less than 10.
I don't see any assumption...the question is "Is there a pair of these tollbooths less than 10 miles apart ?"...the answer is always YES even in your cases. There is ONE pair atleast which is less than 10 miles apart.
As I suspected the assumption is that they are uniformly divided on a highway.
It need not be that way. 1 & 2 can be 5 miles apart and 2 & 3 can be 15 miles apart. Which means 1 & 3 are 20 miles apart.
The other scenario can be
1 - at 0 miles 2 - 7 -miles 3- 18 miles 4 - 25 miles
That is how it is in ASEAN and India. The toll is collected for the road or a bridge. Kindly enlighten me, bit blur here.