Approximating the 5 numbers making up an average.

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I'm looking at emails handled in the workplace and overall have worked out an average handling time of 387 seconds. There are 5 different types of emails that go into this average and there volumes are below;

Email 1 - 12,081 Email 2 - 7,453 Email 3 - 4,475 Email 4 - 2,808 Email 5 - 2,674

Now, assuming each type of email takes the same time to handle is there a way I can work backwards through this and calculate an average handling time for each type?

I know it would be a case of best fit and any help anyone could give me would be great.

Cheers in advance

Ben