Two complicated math riddles I don't know how to solve?

1. In front of you are several long fuses. You know they burn for exactly one hour after you light them at one end. The entire fuse does no necessarily burn at a constant speed. For example, it might take five minutes to burn through half the fuse and fifty-five minutes to burn the other half. With your lighter and... show more 1. In front of you are several long fuses. You know they burn for exactly one hour after you light them at one end. The entire fuse does no necessarily burn at a constant speed. For example, it might take five minutes to burn through half the fuse and fifty-five minutes to burn the other half. With your lighter and using these fuses, how can you measure exactly three-quarters of an hour of time?

2. Diophantus's youth lasted 1/6 of his life. He had his first beard in the next 1/12 of his life. At the end of the following 1/7 Diophantus got married. Five years from then his son was born. His son lived exactly 1/12 of Diophantus's life. Diophantus died 4 years after the death of his son... How long did Diophantus live?

I would much rather you tell me how to do these than just giving me the answers. Thank you for any help!
Update: His son lived 1/2 of Diophantus' life! My mistake.
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