The exit for Hudsonville is 24 miles past the exit for Harper City. A new exit will be added for West Haven that divides the highway from Harper City to Hudsonville in a 3 to 2 ratio. One new road sign will divide the section from West Haven to Hudsonville in a 1 to 1 ratio. Find the distances between all three cities and the locations of both new signs.

The exit for West Haven is located 14.4 miles from Harper City and 9.6 miles from Hudsonville. The new road sign between West Haven and Hudsonville is located halfway, which is 4.8 miles from each city.

Explanation:

You asked about dividing a highway section between two cities, a Mathematics problem involving ratios and distances. The exit for Hudsonville is 24 miles past the exit for Harper City. A new exit for West Haven will split the highway from Harper City to Hudsonville in a 3 to 2 ratio, and another new sign will split the section from West Haven to Hudsonville in a 1 to 1 ratio.

Step-by-step solution:

Let the total distance from Harper City to Hudsonville be 'd' miles. We know that 'd' is 24 miles.
To find out where West Haven should be, we take the ratio 3 to 2, so the distances from Harper City to West Haven to Hudsonville will be 3x and 2x respectively, where 3x + 2x = d.
Solving the equation 5x = 24 gives us x = 24/5 = 4.8 miles. Therefore, West Haven is 3x = 3(4.8) = 14.4 miles from Harper City and 2x = 2(4.8) = 9.6 miles from Hudsonville.
Now, for the new road sign that divides the section from West Haven to Hudsonville in a 1 to 1 ratio, this section is 9.6 miles. So, the sign would be placed 4.8 miles from West Haven and also 4.8 miles from Hudsonville as 9.6 miles / 2 = 4.8 miles.

Distances: 14.4 miles between Harper City and West Haven, 9.6 miles between West Haven and Hudsonville, and 24 miles between Harper City and Hudsonville. The location of the new exit sign for West Haven is 14.4 miles from Harper City. The second sign is 4.8 miles from West Haven towards Hudsonville.