This is the answer to last week’s Problem of the Week:

One thing that I like to do when solving these types of problems is determining what percentage of the work each participant will do. The problem stated that Tasheera takes 16 seconds for each balloon, whereas Omar takes 18 seconds. Knowing this, we can basically calculate the percentage of the work with the following table:

Name Time Comparative Speed Percentage of Work
Tasheera 16 18/16 (18 / 16) / (18 / 16 + 18 / 18) = 9/17
Omar 18 18/18 (18 / 18)(18 / 16 + 18 / 18) = 8/17

After doing this, we can multiply their percentage against the amount of balloons each will blow up:

Name Percentage of Work Balloons
Tasheera (18 / 16) / (18 / 16 + 18 / 18) = 9/17 100 × 9/17 ≈ 53
Omar (18 / 18)(18 / 16 + 18 / 18) = 8/17 100 × 8/17 ≈ 47

Finally we can use the amount of balloons and multiply it by the amount of time it takes per balloon (minus one increment of the rest time) to get the amount of seconds it would take to blow up 100 balloons:

Name Time w/ Rest Rest Time Balloons Total Time (secs)
Tasheera 16 5 53 53 × 16 – 5 = 843
Omar 18 3 47 47 × 18 – 3 = 843

Therefore, the answer is that it would take Tasheera and Omar 843 seconds (14 and 3 seconds) to inflate 100 balloons.

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#### POW – Party Balloons | Chris West's Blog · April 27, 2012 at 2:33 PM

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