A riddle about a drummer has been cited in print since 1858:
 
Q: Why is a drummer the fastest man in the world?
A: Because time beats all men, but the drummer beats time.
 
“Who is the fastest man on earth?—The music teacher. he beats time, you know” was printed in an 1890 newspaper.
   
     
18 December 1858, Albany (NY) Evening Journal, pg. 4, col. 7:   
Why is a drummer the fastest man in the world? Because time beats all men, but the drummer beats time.
     
27 December 1858, The Compiler (Gettysburg, PA), pg. 1, col. 5:
Why is a drummer the fastest man in the world? Because Time beats all men, but the drummer beats time.
   
Google Books
Family Herald
Volume 16
1858
Pg. 720:
A drummer is the fastest man in the world, because time beats all men, but the drummer beats time.
   
Chronicling America
7 January 1859, Bedford (PA) Gazette, pg. 1, col.  6:
Why is a drummer the fastest man in the world? Because Time beats all men, but the drummer beats time.
 
16 September 1868, Bedford County Press (Bloody Run (Everett) PA), “Odds and Ends,” pg. 4, col. 2:
The fastest man—a drummer; he beats time.
 
6 June 1871, Pittsburgh (PA) Gazette, “Facetious Hints to Musicians,” pg. 1, col. 7:
The irrepressible punster of the Boston Commercial Bulletin says:
(...)
You may get many notes from an orchestra, although it don’t go a-loan, but has a leader, generally a very fast man, for he beats time.
 
7 July 1871, Burlington (VT) Weekly Free Press,  “Rules and Suggestions for Musicians,” pg. 1, col. 2:
You may get plenty of notes from an orchestra, although it don’t go a-loan, but has a leader; generally a very fast man for he beats time.
   
28 October 1883, The Enquirer (Cincinnati, OH), pg. 14, col. 4:
The fastest man is the leader of an orchestra. He beats time.
 
18 October 1890, Beverly (MA) Citizen, “Chips,” pg. 4, col. 1:
Who is the fastest man on earth?—The music teacher. he beats time, you know.
   
28 December 1975, Gallup (NM) Independent, “Hal Kaufman’s Junior Whirl,” pg. 22, col. 3:
Riddle-Me-This: Why is a drummer the fastest man in the world? Answer: Because although time beats all men, a drummer beats time. No?
 
Google Books
Old Groaners
By Susan Watkin
Lulu Press (Lulu.com)
2006
Pg. 3:
Why is a drummer the fastest man in the world?
☺ Because time beats everything; but a drummer beats time.