ちょっと私は配列を持っています。各値を区切る必要があるので、次のようになります
$arry = array(a,b,c,d,e,f)
$point1 = (SELECT distance FROM Table WHERE Origin = a AND Destination = b);
$point2 = (SELECT distance FROM Table WHERE Origin = b AND Destination = c);
$point3 = (SELECT distance FROM Table WHERE Origin = c AND Destination = d);
$point4 = (SELECT distance FROM Table WHERE Origin = d AND Destination = e);
$point5 = (SELECT distance FROM Table WHERE Origin = e AND Destination = f);
$point6 = (SELECT distance FROM Table WHERE Origin = f AND Destination = g);
$point7 = (SELECT distance FROM Table WHERE Origin = g AND Destination = f);
$total_trav = $point1+$point2+$point3+$point4+$point5+$point6+$point7