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

Chester to Durbin is 11.9 miles far.

Explanation:

Please refer to the attached figure.

Given:-

Distance from Alston to Barton=
`10(3)/(5) =(50+3)/(5) =(53)/(5)`

Distance from Alston to Barton = 10.6 miles

Distance from Barton to Chester =
`12(1)/(2) =(24+1)/(2) =(25)/(2)`

Distance from Barton to Chester = 12.5 miles

Distance from Alston to Durbin = 35 miles.

To find:- Distance from Chester to Durbin = ?

Solution:-

Let Alston=A, Barton=B, Chester=C, Durbin=D.

Now from the attached figure we can see that,

A to B is the distance from Alston to Barton,

`\therefore\ AB=10.6\ miles`

B to C is the distance from Barton to Chester,

`\therefore\ BC=12.5\ miles`

A to is the distance from Alston to Durbin,

`\therefore\ AD=35 miles`

C to D is the distance from Chester to Durbin

`\therefore` We have to find Distance CD=?

Now from the attached figure we can see that,

`CD=AD-AC`

`CD=AD-(AB+BC)`

`CD=35-(10.6+12.5)`

`CD=35-23.1`

`CD=11.9\ miles`

As CD is the distance from Chester to Durbin,

Therefore Chester to Durbin is 11.9 miles far.