Rank function with multiple criteria

Hello...first post so be gentle!
I am a paraglider pilot and want to set up an automated rank sheet of the paragliders I have flown showing which has flown most. In the simplified example (attached) I have used the rank and countif functions to rank the data by hours. However, this assigns duplicated places solely on their position in the list. I am trying to do a better job with tied results using the next column which shows how many flights the paraglider has done. It is easy to do this using data>sort> and using different levels. However, this does not seem to be immediately possible automatically using the RANK function.

Can anyone help or point me in the right direction? Thank you!

Thank you Marvin. Your very elegant & simple answer neatly solves the problem I posed. However, it doesn't actually solve the unsimplified problem! With more complex data it does not work. I need to rank the data primarily by column C and then by Column D if a tie exists. Merging the data doesn't do that.

Ok, all sorted now, thanks to Marvin. I just needed to adjust his "helper" function so as not to interfere too much with the data:
=(c2*100)+d2/1000

Hello again Marvin,

Your last suggestion is not an automatic function, unless I'm misunderstanding you.

Your solution alters the data quite a lot and produces a rank that isn't always based on column C first. My slight adaptation reduces the importance of the tie breaker addition so doesn't alter the primary criterion. I've attached a bit more of my spreadsheet so you can see for yourself.

Anyway, it's solved now and all down to you, so thank you for your time!

I should add that in the final version, columns E to I are hidden.

This should work without a helper column.

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Enter in cell A4 on your original spreadsheet then drag down. I've tested it against your most recent attachment and it produces the same results.