Weighted Average of Sequential Time Based Data Series Using Start/End Time Input

Hi everyone! I am new to this forum. I would consider myself intermediate level excel.

I am looking to calculate a weighted average of sequential time based data based on an input start and end time. The excel formula should use a start and end time as input, find the relative data in the sequential time sorted data array, and return the weighted average of the "rate" based on the appropriate data.

The data contains a sumproduct row based on the "rate" and "t2-t1" (delta time). I have included a sample data sheet which has the Input, the Expected Answer, a sample Data Base, and a manual calculation of the answer.

I originally did this using a macro, but I am looking for something simpler using functions. Pretty sure this could be done with MATCH or VLOOKUP but can't find the right fit yet.

Any help is appreciated!

See attached excel example!