Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of pump required depends on the depth of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of D2 + 4D – 250 gallons per minute, pumping out a mine that is 25 150 feet deep would require a pump that pumps a minimum of how many gallons per minute?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
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Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Understanding Pump Capacity for Abandoned Mines**
Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of pump required depends on the depth of the mine. If pumping out a mine that is \( D \) feet deep requires a pump that pumps a minimum of
\[
\frac{D^2}{25} + 4D - 250
\]
gallons per minute, pumping out a mine that is 150 feet deep would require a pump that pumps a minimum of how many gallons per minute?
**Options:**
- 362
- 500
- 1,750
- 800
- 1,250
**Solution:**
To find the minimum pump capacity required for a 150 feet deep mine, substitute \( D = 150 \) into the formula:
\[
\frac{150^2}{25} + 4 \times 150 - 250
\]
Calculate each part:
- \(\frac{150^2}{25} = \frac{22500}{25} = 900\)
- \(4 \times 150 = 600\)
Then, add and subtract the values:
\[
900 + 600 - 250 = 1250
\]
The correct answer is **1,250** gallons per minute.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40ac1924-da82-497b-85f4-398551157699%2F70b7e82b-ebe9-4378-a4da-4c7730ead3c7%2Frw15iut_processed.jpeg&w=3840&q=75)
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