Question

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?

Answer 1

Durbin is
`11(9)/(10)\:miles` far from Chester.

Explanation:

Distance Between Alston and Barton =
`10(3)/(5)\:miles`

Distance Between Barton and Chester =
`12(1)/(2)\:miles`

Distance Between Alston and Durbin =
`35\:miles`

Distance between Chester and Durbin =
`35-10(3)/(5)-12(1)/(2)`

=
`35-(53)/(5)-(25)/(2)`

=
`(350-106-125)/(10)`

=
`(119)/(10)`

=
`11(9)/(10)\:miles`

Therefore, Durbin is
`11(9)/(10)\:miles` far from Chester.

Answer 2

see the picture attached to better understand the problem

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

we know that

`10 (3)/(5) = ((10*5+3))/(5) \\ \\ = (53)/(5) miles`


`12 (1)/(2) = ((12*2+1))/(2) \\ \\ = (25)/(2) miles`


`10 (3)/(5) +12 (1)/(2) +x=35`
subtitute


`(53)/(5) + (25)/(2) +x=35`

solve for x


`x=35-( (53)/(5)+ (25)/(2) ) \\ \\ x=35- ((2*53+5*25))/(10) \\ \\ x=35- (231)/(10) \\ \\ x=35-23.10 \\ \\ x=11.9`


`x=11 (9)/(10)` miles

the answer is

`11 (9)/(10)` miles