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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?

Verified Answer :

calculista

see the picture attached to better understand the problem

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

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

\(12 \frac{1}{2} = \frac{(12*2+1)}{2} \\ \\ = \frac{25}{2} miles\)

\(10 \frac{3}{5} +12 \frac{1}{2} +x=35\)
subtitute

\(\frac{53}{5} + \frac{25}{2} +x=35\)

solve for x

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

\(x=11 \frac{9}{10}\) miles

the answer is
\(11 \frac{9}{10}\) miles


View image calculista

Answer:

Durbin is \(11\frac{9}{10}\:miles\) far from Chester.

Step-by-step explanation:

Distance Between Alston and Barton = \(10\frac{3}{5}\:miles\)

Distance Between Barton and Chester = \(12\frac{1}{2}\:miles\)

Distance Between Alston and Durbin = \(35\:miles\)

Distance between Chester and Durbin = \(35-10\frac{3}{5}-12\frac{1}{2}\)

                                                                 = \(35-\frac{53}{5}-\frac{25}{2}\)

                                                                 = \(\frac{350-106-125}{10}\)

                                                                 = \(\frac{119}{10}\)

                                                                 = \(11\frac{9}{10}\:miles\)

Therefore, Durbin is \(11\frac{9}{10}\:miles\) far from Chester.

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