Answered

Get expert advice and insights on any topic with IDNLearn.com. Our experts are ready to provide in-depth answers and practical solutions to any questions you may have.

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?

Sagot :

Calculistaidn
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


View image Calculista

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.

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.