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.

## 1 Comment

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

[…] answer to this Problem of the Week can be found here. This entry was posted in Blog, Math, Problem of the Week and tagged Math, Problem of the Week by […]