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What is the supposed speed for a MPLS (4.5M)?

We have a MPLS connection (4.5m) between two sites. The distance between two sites is probably 500 miles.

During the off-hours we conducted three ping tests. Each with 100 pings. The result as follows:
#1 ping the remote site using internal IP (via MPLS), response 52 ms
#2 ping the remote site public IP (via Internet), the response 51 ms
#3 ping 8.8.8.8, the average response 33 ms

The above result just puzzles me. Can you please help understand the following:
1. MPLS is supposed to be much faster than Internet, correct? Then why above #1 is virtually of no difference from #2?
2. Why our site-to-site, whether MPLS or Internet, is much slower than to 8.8.8.8?
3. What is the supposed speed for a MPLS (4.5M) spanning 500 miles?

Thank you for your help.

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R_Edwards

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SJCA

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Castlewood

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"2. when you ping from site-to-site, the packets are routed from different hops (ISPs) to your destination."

But tracert shows the site-to-site with 4 hops while 8.8.8.8 with 13 hops. So isn't the site-to-site supposed to be faster than the 8.8.8.8?

Also, since tracert shows 4 hops for MPLS, does it mean there is NO other ISPs involved in our MPLS connection?