Calculating average combined speed of unequal ratios

Hope someone can help with this.

Department 'A' answered 1,502 phone calls at an average answer speed of 0.01 seconds.
Department 'B' answered 890 phone calls at an average answer speed of 8.20 seconds.
The total calls answered was 2392. Department 'A' answered 62.8% of the calls and Department 'B' answered 37.2%.
What is the combined average answer speed of both Departments 'A' and 'B?'

I know that if Departments 'A' and 'B' each answered an equal number of calls, the formula would be:

8.20 + 0.01
----------- = 4.11 seconds
2

but it's not a 50/50 ratio. What formula would I use to account for the 63/37 split?

Quote:

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Originally Posted by StJames

Department 'A' answered 1,502 phone calls at an average answer speed of 0.01 seconds.

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Speed is not measured in seconds. You probably mean seconds per call. Find the total number of seconds and divide it by the total number of calls. The formula can be simplified when you know the percentages of calls made by the two departments, but this is the next step.

You are right that you cannot "average" things that way.
Department A answered 1502 calls in an average time of 0.01 seconds.
So department A answered 1502 calls in a total time of (1502)(.01)= 15.02 seconds

Department B answered 890 calls in an average time of 8.20 seconds.
So department B answered 890 calls in an total time of (890)(8.20)= 7298.

Over all then the two departments answered 1502+ 890= 2392 calls in 15.02+ 7298= 7313.02 seconds
So what is average time per call?

You could also do a "weighted" average .628(0.01)+ .372(8.20).
(Those won't give exactly the same answer because of round off in calculating the percentages.)

Many, many thanks!