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Q1-58P.

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Found in: Page 19

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# Question: Why is the following situation impossible? In an effort to boost interest in a television game show, each weekly winner is offered an additional $1 Million bonus prize if he or she can personally count out that exact amount from a supply of one-dollar bills. The winner must do this task under supervision by television show executives and within one 40 hours work week. To the dismay of the show’s producers, most contestants succeed at the challenge. Answer It takes 6:9 Weeks . So It is not possible to count the$ 1 million dollar in one 40 Hour work week.

See the step by step solution

## Step 1: Finding the time interval required for the task

Write the equation for the time required to complete the task, if the winner counts the dollar per second without stopping.

Here \$ Million dollars are equal to 1000000 dollars

Available data:

• .$1\text{h}=3600\text{s}$
• $1\text{work}\text{week}=\text{40}\text{h}$.

Then we can calculate the time taken to count money as

$T=1000000×\left(\frac{1 s}{1}\right)×\left(\frac{1\text{h}}{3600\text{s}}\right)×\left(\frac{1\text{work}\text{week}}{\text{40}\text{h}}\right)\phantom{\rule{0ex}{0ex}}={10}^{6}×\left(\frac{1\text{s}}{1}\right)×\left(\frac{1\text{h}}{3600\text{s}}\right)×\left(\frac{1 \text{work} \text{week}}{\text{40} \text{h} }\right)\phantom{\rule{0ex}{0ex}}=\frac{1000000}{144000}\text{work}\text{weeks}\phantom{\rule{0ex}{0ex}}=\text{6.94}\text{work}\text{weeks}\phantom{\rule{0ex}{0ex}}$

Here is the time required for the task.

## Step 2: Deriving the final solution

Therefore this task needs . As it needs a long time, it is impossible to complete the task within the time limit. Because the time limit given by the television executive is one work week, it takes more than one work week.

Thus, it takes 6.9 Weeks. So It is not possible to count the dollar in one 40 hour work week.