It is 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via Barton and Chester is 35 miles. How far is it from Chester to Durbin?

see the picture attached to better understand the problem

Let
x----------> The distance from Chester to Durbin

we know that
[tex]10 \frac{3}{5} = \frac{(10*5+3)}{5} \\ \\ = \frac{53}{5} miles[/tex]

[tex]12 \frac{1}{2} = \frac{(12*2+1)}{2} \\ \\ = \frac{25}{2} miles [/tex]

[tex]10 \frac{3}{5} +12 \frac{1}{2} +x=35[/tex]
subtitute

[tex] \frac{53}{5} + \frac{25}{2} +x=35[/tex]

solve for x

[tex]x=35-( \frac{53}{5}+ \frac{25}{2} ) \\ \\ x=35- \frac{(2*53+5*25)}{10} \\ \\ x=35- \frac{231}{10} \\ \\ x=35-23.10 \\ \\ x=11.9 [/tex]

[tex]x=11 \frac{9}{10}[/tex] miles

the answer is
[tex]11 \frac{9}{10} [/tex] miles

Aquialaskaid Aquialaskaid · Answer 2

Answer:

Durbin is [tex]11\frac{9}{10}\:miles[/tex] far from Chester.

Step-by-step explanation:

Distance Between Alston and Barton = [tex]10\frac{3}{5}\:miles[/tex]

Distance Between Barton and Chester = [tex]12\frac{1}{2}\:miles[/tex]

Distance Between Alston and Durbin = [tex]35\:miles[/tex]

Distance between Chester and Durbin = [tex]35-10\frac{3}{5}-12\frac{1}{2}[/tex]

= [tex]35-\frac{53}{5}-\frac{25}{2}[/tex]

= [tex]\frac{350-106-125}{10}[/tex]

= [tex]\frac{119}{10}[/tex]

= [tex]11\frac{9}{10}\:miles[/tex]

Therefore, Durbin is [tex]11\frac{9}{10}\:miles[/tex] far from Chester.