As I was doing my co-worker’s system administrative tasks last month, I always was asked this question why one of client server is having slow speed issues. Well who knows until you check try to solve the problem 
Few things you can always do to check for bandwidth and network analysis.
Install IPTraf – IPTraf is a console-based network statistics utility for Linux. It gathers a variety of figures such as TCP connection packet and byte counts, interface statistics and activity indicators, TCP/UDP traffic breakdowns, and LAN station packet and byte counts.
yum install iptraf -y
Install vnStat – vnStat is a network traffic monitor for Linux that keeps a log of daily network traffic for the selected interface. vnStat isnt a packet sniffer. The traffic information is analyzed from the /proc -filesystem, so vnStat can be used without root permissions.
cd /usr/local/src wget http://humdi.net/vnstat/vnstat-1.6.tar.gz tar -zxvf vnstat-1.6.tar.gz cd vnstat-1.6 make && make install vnstat -u -i eth0
vnstat --help
Check Apache connection and always check for DDOS attacks.
If your server is WHM / CPanel configured always check bandwidth usage from WHM / CPanel and do the comparing.
Above will give few ideas whats happening on server, and actually you can come up with solution based on these few basic in house tasks.
