Rendezvous
In which town should five friends meet, in order to keep the total travelling distance as small as possible?
Problem
Bergerac | ||||
$87$ | Bordeaux | |||
$79$ | $47$ | Langon | ||
$61$ | $31$ | $54$ | Libourne | |
$58$ | $84$ | $37$ | $65$ | Marmande |
The table shows the distance (in km) between five towns in southern France.
Five friends live in these five towns and want to meet.
In which of these towns should they meet to keep the total travelling distance as small as possible?
Student Solutions
If the friends meet in Bergerac, the total distance travelled will be $$87+79+61+58 \; \text{km} = 285\; \text{km}$$
Bergerac | ||||
$87$ | Bordeaux | |||
$79$ | Langon | |||
$61$ | Libourne | |||
$58$ | Marmande |
If the friends meet in Bordeaux, the total distance travelled will be $$87+47+31+84 \; \text{km} = 249\; \text{km}$$
Bergerac | ||||
$87$ | Bordeaux | |||
$47$ | Langon | |||
$31$ | Libourne | |||
$84$ | Marmande |
If the friends meet in Langon, the total distance travelled will be $$79+47+54+37 \; \text{km}=217\; \text{km}$$
Bergerac | ||||
Bordeaux | ||||
$79$ | $47$ | Langon | ||
$54$ | Libourne | |||
$37$ | Marmande |
If the friends meet in Libourne, the total distance travelled will be $$61+31+54+65 \; \text{km}=211\; \text{km}$$
Bergerac | ||||
Bordeaux | ||||
Langon | ||||
$61$ | $31$ | $54$ | Libourne | |
$65$ | Marmande |
If the friends meet in Marmande, the total distance travelled will be$$58+84+37+65 \; \text{km}=244\; \text{km}$$
Bergerac | ||||
Bordeaux | ||||
Langon | ||||
Libourne | ||||
$58$ | $84$ | $37$ | $65$ | Marmande |
So the friends should meet in Libourne.