We have towns A, B, and C, with a straight highway connecting towns A and C, which is 60 miles long. The straight-line distance from A to B is 50 miles, and the straight-line distance from B to C is 50 miles.

The highway connecting A and C can be thought of as the hypotenuse of a right triangle, where the legs of the triangle are the distances from A to B and from B to the point on the highway (let's call it point D).

The triangle formed by points A, B, and D is similar to the triangle formed by points A, B, and C because they share the same angles. This is because vertical angles (formed by the highway and the straight-line distances) are congruent.

We can set up a proportion to find the distance from B to D:

BD/BC =​ AB/AC
Substituting the given values:

BD/60 = 50/100 (50 miles is half of 100 miles)

Now, solving for BD:

BD = 30 miles

So, the distance from town B to the point on the highway connecting towns A and C, which is closest to town B, is 30 miles.