Yes, it is possible in 17 minutes. Here is how it works: 
1 2 5 10 ---- _ _ _ __ total = 0
_ _ 5 10 ---- 1 2 _ __ total = 2
1 _ 5 10 ---- _ 2 _ __ total = 3
1 _ _ __ ---- _ 2 5 10 total = 13
1 2 _ __ ---- _ _ 5 10 total = 15
_ _ _ __ ---- 1 2 5 10 total = 17.
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