SOLUTION: Four cities lie along a straight highway in the order of city A B C and D. the distance from city A to city B is five times the distance from city B to city CD. The distance from

Question 1046349: Four cities lie along a straight highway in the order of city A B C and D. the distance from city A to city B is five times the distance from city B to city CD. The distance from city A to city D is two times The distance from city A to city B the distance between cities C to D is 10 miles. What is the distance between city AB?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There are typos in that question.
I am guessing the question meant states:
The distance from city A to city B is five times the distance from city B to city C.
The distance from city A to city D is two times the distance from city A to city B.
The distance between cities C to D is 10 miles.

A SHORT WRITE UP:

The distance between city A and city B is .

A LONGER EXPLANATION, WITH A VARIABLE SO IT LOOKS MORE LIKE ALGEBRA:
Let us define a variable .
= the distance from city B to city C, in miles.
(We could call it , but is shorter).
Since the distance from city A to city B is five times the distance from city B to city C,
the distance from city A to city B is .
The distance from A to C must be the sum of the two distances listed above:
.
So far we have this picture:

We also know that the distance from city A to city D is two times the distance from city A to city B.
So, th2 distance from city A to city D is
,
and we know that the distance between cities C to D is 10 miles.
Now, the picture looks like this:
.
Considering the distances shown by the arrows
between A and C , and a
between A and D ,
the distance between C and D must be their difference
.
Now, we can represent the situation as

Finally since the distance, in miles, between C and D is and ,

is the distance, in miles, between B and C,
and the distance, in miles, between A and B is

.
The distance between city A and city B is .

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