## System Upgrade

#### Problem

During an automated daily task a computer spends 20% of the time importing the raw data from thousands of text files, 70% of the time processing it, and 10% of the time exporting the results to spreadsheet files and archiving the data.

To help speed-up the task a new chip is purchased that will double the speed of the processing task and the newly purchased hard drives allow both import and export times to be reduced by 30%.

How much time will be saved overall and what percentage of the time will be spent doing each of importing, processing, and exporting the data?

#### Solution

When we are not given actual times it is often convenient to work with an initial value of 100 so that final percentage changes can be compared more easily.

On the old system, the computer took 70 units of time to complete the processing part of the task; the new chip doubles the processing speed, so it will now complete in 35 units of time.

It took 30 units of time to import and export the data. But because the new drives reduce import and export time by 30%, it will complete in 70% of the previous time. And as 10% of 30 is 3, it will now take 21 units of time.

Hence the new system will take 35 + 21 = 56 units of time to complete the task, which represents an overall reduction of 44% in the time taken to complete the task.

After the upgrade, the ratio of times to complete each part of the task is,

import : process : export = 14 : 35 : 7 = 2 : 5 : 1

That is, the computer spends 2 + 5 + 1 = 8 units of time to complete the task of which it spends 2/8 = 25% of the time importing data, 5/8 = 62.5% of the time processing data, and 1/8 = 12.5% of the time exporting data.