Respuesta :
Dividing the segments and finding the lengths, it is found that the distance between the two cities is of 130 miles.
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- We want to find the distance between cities a and d.
- Due to the cities along the highway, the distance is given by:
[tex]ad = ab + bc + cd[/tex]
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- The distance from city a to city b is 5 times the distance from city b to city c, and thus:
[tex]ab = 5bc[/tex]
In terms of x, [tex]bc = x, ab = 5x[/tex]
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- The distance from city b to city c is 2 times the distance from city c to city d, and thus:
[tex]bc = 2cd[/tex]
In terms of x, [tex]cd = \frac{x}{2}[/tex]
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- The distance between city d and city c is 10 miles, thus:
[tex]\frac{x}{2} = 10[/tex]
[tex]x = 20[/tex]
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- The other distances are:
[tex]bc = x = 20[/tex]
[tex]ab = 5x = 5(20) = 100[/tex]
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- The distance between cities a and d is:
[tex]ad = ab + bc + cd = 100 + 20 + 10 = 130[/tex]
The distance between the two cities is of 130 miles.
A similar problem is given at https://brainly.com/question/24352869
