Expert: Josh - 4/25/2005

Question
Hello
I wondered if you could help us with this maths problem as the whole family are arguing about the way to work it out!
Thanks Lee

Two cars start off at the same point on a straight road facing opposite directions. Each car drives for six miles, takes a left turn, and drives for eight miles. How far apart are the two cars?
2 miles
11 miles
14 miles
20 miles
26 miles  

Answer
Hi Lee,

Let's say that both cars (x1 and X2) start at point E.
x1 faces point B. x2 faces point H.
The route followed by x1 is given by EB,BA, where distance |EB|=6 miles, |BA|=8 miles.
The route followed by x2 is given by EH,HI, where distance |EH|=6 miles, |HI|=8 miles.

Their separation is given by |AI|=|AE|+|EI|.
You should note that |AE|=|EI|, since the problem is symmetrical (both drivers drive at the same speed).
Distance |AE|=sqrt(|AB|^2+|BE|^2) using pythagoras theorem.
|AE|=sqrt(6^2+8^2)=sqrt(36+64)=10 miles
Therefore, |EI|=10 miles also.

The two cars are 20 miles apart (adding |AE| and |EI|).

A-----B-----C
.
.
D-----E-----F
.
.
G-----H-----I

Cheers.