Question

it is 10 3/5 miles of 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

so 10 and 3/5 ferom alston to barton
12 and 1/2 from barton to chester
from alston to durbin=35
it says that bartonand chester is between alston and durbin therefoe
 the distances are
alston-----10 and 3/5-----barton----12 and 1/2-----chester----x---durbin
|----------------------------------35----------------------------------------------------|
therefor

10 and 3/5+12 and 1/2+x=35

first we need to add 10 and 3/5 and 12 and 1/2
10 and 3/5=10 and 6/10
12 and 1/2=12 and 5/10
10 and 6/10+12 and 5/10=22 and 11/10=23 and 1/10
23 and 1/10+x=35
subtract 23 and 1/10 from both sides
x=11 and 9/10

the answer is 11 and 9/10 miles

Answer 2

We know that out of the 35 miles distance from Alston to Durbin via Barton and Chester, that the total miles it took to get to Chester from Alston via Barton was the total miles from adding 10 3/5 and 12 1/2 miles. So we only have to add 10 3/5 with 12 1/2 and then subtract the total from 35, which will give usu the remaining possible miles, to find the distance between Chester and Durbin. I've drawn and attached a map to help you visualize and understand the concept better.

 10 3/5 + 12 1/2 = 23 1/10  (note that you had to find a common denominator, which I wrote as 10.)

35 - 23 1/10 = 11 9/10

11 9/20 ⇒ 11.9

So the distance from Durbin to Chester is 11 9/10 miles, or 11.9 if you want decimals.