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r - Deleting rows that are duplicated in one column based on the conditions of another column

Here is an example of my data set;

Date      Time(GMT)Depth Temp  Salinity Density Phosphate
24/06/2002  1000    1           33.855          0.01
24/06/2002  1000    45          33.827          0.01
01/07/2002  1000    10  13.26   33.104  24.873  0.06
01/07/2002  1000    30  12.01   33.787  25.646  0.13
08/07/2002  1000    5   13.34   33.609  25.248  0.01
08/07/2002  1000    40  12.01   34.258  26.011  1.33
15/07/2002  1000    30  12.04   34.507  26.199  0.01
22/07/2002  1000    5   13.93   33.792  25.269  0.01
22/07/2002  1000    30  11.9    34.438  26.172  0.08
29/07/2002  1000    5   13.23   34.09   25.642  0.01

I want to delete duplicate rows so that I only have one row per date, I want to do this based on the Depth, I would like to keep the row with the greatest (deepest) depth. Any ideas?

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Lets say you have data in df

df = df[order(df[,'Date'],-df[,'Depth']),]
df = df[!duplicated(df$Date),]

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