Question

On average, water flows over a particular water fall at a rate of 2.02 x 105 cubic feet per second. One cubic foot of water weighs
62.4 lb. Calculate the rate of water flow in tons of water per day. (1 ton = 2200 lb)
2.40e15
tons/day
the tolerance is +/-2%

Answer 1

Answer:

Approximately 5.00 × 10⁸ tons per day. (Rounding error: less than 1.1%.)

Explanation:

How many cubic feet of water flows over this waterfall each day?

The question gives only the number of cubic feet of water that flows over each second. To find the volume for each day, start by finding the number of seconds in a day.

There are 60 seconds in a minute and 60 minutes in an hour. That translates to $60 \times 60$ seconds in an hour.

There are 24 hours in a day. Each hour contains $60 \times 60$ seconds. That means that there are $24 \times 60 \times 60$ seconds in a day.

$2.02 \times 10^{5}$ cubic feet of water flows over this waterfall every second. Therefore, $24 \times 60 \times 60\times 2.02 \times 10^{5}$ cubic feet of water flows over this waterfall every day.

The weight of one cubic foot of water is $62.4$ pounds. The weight of $24 \times 60 \times 60\times 2.02 \times 10^{5}$ of cubic feet of water will be $24 \times 60 \times 60\times 2.02 \times 10^{5}\times 62.4$ pounds.

It takes 2,200 pounds to make a ton.   $24 \times 60 \times 60\times 2.02 \times 10^{5}\times 62.4$ will translate to $\displaystyle \frac{1}{2200}\times 24 \times 60 \times 60\times 2.02 \times 10^{5}\times 62.4$ tons.

To calculate the rounding error, evaluate

$\displaystyle \frac{\text{Rounded Value} - \text{Actual Value}}{\text{Actual Value}}\times 100\%$ and drop the negative sign if there is one. Rounding the final result to $5.00\times 10^{5}$ gives a rounding error of approximately $1.0\%$.