Of course, the old fashion hash is always here to help

use warnings;
use strict;

my $router_route = {};    ## an hash ref
my $name         = "";
while (<DATA>) {
    s{^\s+|\s+$}{};       # remove the first and trailing spaces
    if (/^traceroute to.+?\((.+?)\).+?$/s) {
        $name = $1;
    }
    ++$router_route->{$name} if /^\d/;
}
print "ROUTE\t\t\tNUMBER OF HOPS\n";
my $grand_total_hops = 0;
foreach my $route ( keys %{$router_route} ) {
    $grand_total_hops += $router_route->{$route};
    printf "%s\t\t%s\n", $route, $router_route->{$route};
}
print "\nTOTAL HOPS\t\t", $grand_total_hops, $/;


__DATA__
Traceroute: 11 1291796822 1291796821 1291796821 OpenDNS 0.chstatic.cvc
+dn.com 216.137.61.109
traceroute to 216.137.61.109 (216.137.61.109), 30 hops max, 60 byte pa
+ckets
 1  192.168.178.1  0.638 ms  7.361 ms  7.366 ms
 2  82.135.16.28  44.925 ms  46.633 ms  50.457 ms
 3  212.18.7.121  98.010 ms  98.307 ms  98.650 ms
 4  212.18.6.97  68.374 ms  72.222 ms  76.184 ms
 5  62.140.24.49  129.246 ms  130.224 ms  130.221 ms
 6  4.69.134.2  98.205 ms  105.207 ms  102.287 ms
 7  4.69.140.10  106.816 ms  82.609 ms 4.69.140.2  88.631 ms
 8  4.68.23.76  79.559 ms  65.093 ms 4.68.23.204  64.530 ms
 9  212.162.24.70  65.476 ms  50.797 ms  55.108 ms
10  216.137.61.109  58.221 ms  62.351 ms  59.094 ms
Query: 18 1291796822 GoogleDNS 0.chstatic.cvcdn.com 1 True 0.155671834
+946 0.0507638454437
Traceroute: 2 1291796823 1291796822 1291796822 LocalDNS LocalDNS 192.1
+68.178.1
traceroute to 192.168.178.1 (192.168.178.1), 30 hops max, 60 byte pack
+ets
 1  192.168.178.1  0.649 ms  1.033 ms  1.013 ms
Query: 13 1291796823 LocalDNS 0.media.collegehumor.com 1 True 0.193642
+139435 0.0472960472107
Traceroute: 9 1291796827 1291796822 1291796822 GoogleDNS GoogleDNS 8.8
+.8.8
traceroute to 8.8.8.8 (8.8.8.8), 30 hops max, 60 byte packets
 1  192.168.178.1  0.464 ms * *
 2  82.135.16.28  68.613 ms  72.079 ms  76.268 ms
 3  212.18.7.101  160.966 ms  163.495 ms  163.517 ms
 4  93.104.240.53  99.638 ms  103.396 ms  108.241 ms
 5  209.85.241.110  111.919 ms 209.85.240.64  114.900 ms 209.85.241.11
+0  119.654 ms
 6  209.85.254.116  124.134 ms 209.85.254.118  127.998 ms 209.85.254.1
+12  111.621 ms
 7  209.85.249.166  116.258 ms 209.85.254.126  115.774 ms 209.85.254.1
+34  105.670 ms
 8  8.8.8.8  95.428 ms  95.573 ms  95.923 ms
Query: 10 1291796827 OpenDNS 1.im.cz 1 True 0.0573320388794 0.05522108
+078
[download]

ROUTE            NUMBER OF HOPS
216.137.61.109        10
8.8.8.8        8
192.168.178.1        1

TOTAL HOPS        19
[download]