6 deleted 1 character in body
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Ruby - 131 115 107 9797 84 bytes

I'm still golfing it.

a=getsh,m,s=gets.split(/\w/).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#to_i;$><<"#{t(h+m/z%2460+s/3600)%24}:#{t%z(m+s/k%k60)%60}:#{t%z%ks%60}"

Thanks for @Doorknob for /\w/ inshead of /h|m|s/

Ruby - 131 115 107 97 bytes

I'm still golfing it.

a=gets.split(/\w/).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#{t/z%24}:#{t%z/k%k}:#{t%z%k}"

Thanks for @Doorknob for /\w/ inshead of /h|m|s/

Ruby - 131 115 107 97 84 bytes

I'm still golfing it.

h,m,s=gets.split(/\w/).map &:to_i;$><<"#{(h+m/60+s/3600)%24}:#{(m+s/60)%60}:#{s%60}"

Thanks for @Doorknob for /\w/ inshead of /h|m|s/

5 deleted 1 character in body
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Ruby - 131 115 107 10097 bytes

I'm still golfing it.

a=gets.split(/h|m|s\w/).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#{t/z%24}:#{t%z/k%k}:#{t%z%k}"

Thanks for @Doorknob for /\w/ inshead of /h|m|s/

Ruby - 131 115 107 100 bytes

I'm still golfing it.

a=gets.split(/h|m|s/).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#{t/z%24}:#{t%z/k%k}:#{t%z%k}"

Ruby - 131 115 107 97 bytes

I'm still golfing it.

a=gets.split(/\w/).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#{t/z%24}:#{t%z/k%k}:#{t%z%k}"

Thanks for @Doorknob for /\w/ inshead of /h|m|s/

4 deleted 1 character in body
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Ruby - 131 115 107107 100 bytes

I'm still golfing it.

a=gets.tr('ms',?h).split(?h/h|m|s/).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#{t/z%24}:#{t%z/k%k}:#{t%z%k}"

Ruby - 131 115 107 bytes

I'm still golfing it.

a=gets.tr('ms',?h).split(?h).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#{t/z%24}:#{t%z/k%k}:#{t%z%k}"

Ruby - 131 115 107 100 bytes

I'm still golfing it.

a=gets.split(/h|m|s/).map &:to_i;k=60;z=k*k;t=a[0]*z+a[1]*k+a[2];$><<"#{t/z%24}:#{t%z/k%k}:#{t%z%k}"
3 deleted 1 character in body
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2 deleted 21 characters in body
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