Chapter EH, Problem 32R

Solution

Interpretation: If 123000 aluminum cans are recycled per minute. The mass of aluminum recycled in September needs to be estimated.

Concept Introduction: In the given question, the number of aluminum cans recycled per minute is given and the mass of one aluminum can is also given; thus, the mass of aluminum cans recycled per month can be calculated by first converting the number of aluminum cans from per minute to per month and simply multiplying the two values.

  $74390400\text{ kg}$

According to the question, 123000 aluminum cans are recycled per minute. Each can have a mass of 14 g. The mass of aluminum in one can is given 14 g. Since the number of aluminum cans recycled per minute is 123000 thus, the number of aluminum cans recycled in September can be calculated as follows:

There are 30 days in September month. The total number of minutes in this month will be:

  $30\text{ days}\left(\frac{24\text{ h}}{1\text{ day}}\right)\left(\frac{60\text{ min}}{1\text{ h}}\right)$

Or,

  $43200\text{ min}$

Since the number of aluminum cans recycled in 1 min is 123000, thus, the number of aluminum cans recycled in 43200 min will be:

  $\begin{array}{c}n=43200\times 123000\\ =5313600000\end{array}$

Now, the total mass of aluminum recycled can be calculated as:

  $\begin{array}{c}m=\frac{14\text{ g}}{1\text{ can}}\times 5313600000\text{ cans}\\ \text{=}74390400000\text{ g}\left(\frac{{10}^{-3}\text{ kg}}{1\text{ g}}\right)\\ =74390400\text{ kg}\end{array}$

Therefore, the mass of aluminum recycled in the month of September is $74390400\text{ kg}$ .