Question

MAPS On a map, Wilmington Street, Beech Drive, and Ash Grove Lane appear to all be parallel. The on

Answer 1

The distance between the two streets along Kendall is 347.9 feet.

Solution:

The image of the problem is attached below.

Distance between Wilmington to Ash Grove along Kendall = 820 feet

Distance between Wilmington to Ash Grove along Magnolia = 660 feet

Distance between Beech and  Ash Grove along Magnolia = 280 feet

Distance between Wilmington to Beech along Magnolia

                                       = 660 feet – 280 feet

                                       = 380 feet

Let us x be the distance between Wilmington to Beech along Kendall and

820 – x be the distance between Beech and  Ash Grove along Kendall.

The given streets are parallel.

By proportionality theorem, parallel lines cut by a transversal are in proportion.

$\Rightarrow\frac{380}{280} =\frac{x}{820-x}$

Do cross multiplication.

$\Rightarrow{380}({820-x}) =280x$

$\Rightarrow 311600-380x =280x$

$\Rightarrow 311600 =280x+380x$

$\Rightarrow 311600 =660x$

$\Rightarrow x=472.1$

Distance between Beech and  Ash Grove along Kendall          

                                    = 820 – x  

                                    = 820 – 472.1

                                    = 347.9

Hence the distance between the two streets along Kendall is 347.9 feet.