A submarine was 200 feet below sea level. It rose to the surface and then dove again to four times its initial depth. The submarine then descended another 300 feet. What was the sub's final depth?
Steps:
$-200+200+4(-200)+(-300)$
1. Write an expression to model the situation.
2. Evaluate the expression. feet
Answer (1)
The submarine starts at a depth of -200 feet.
It rises 200 feet to the surface: − 200 + 200 = 0 feet.
It dives to four times its initial depth: 4 × ( − 200 ) = − 800 feet.
It descends another 300 feet: − 800 − 300 = − 1100 feet. The final depth is − 1100 feet.
Explanation
Understanding the Problem Let's break down the submarine's journey step by step to find its final depth. We'll start with its initial position and track each movement.
Initial Depth The submarine starts at 200 feet below sea level, which we can represent as -200 feet.
Rising to the Surface It then rises to the surface. Rising means moving upwards, so we add 200 feet to its depth: − 200 + 200 = 0 This means the submarine is now at sea level.
Diving to Four Times Initial Depth Next, the submarine dives to four times its initial depth. The initial depth was -200 feet, so four times that depth is: 4 × ( − 200 ) = − 800 The submarine is now at -800 feet.
Descending Another 300 Feet Finally, the submarine descends another 300 feet. Descending means moving further down, so we subtract 300 feet from its current depth: − 800 − 300 = − 1100
Final Depth Therefore, the submarine's final depth is -1100 feet.
Examples
Understanding depth changes like this is useful in many real-world scenarios. For example, engineers designing underwater vehicles need to calculate depth changes to ensure the vehicle can operate safely. Similarly, marine biologists studying ocean life need to understand how different depths affect marine organisms. Even in recreational activities like scuba diving, knowing how depth affects pressure and buoyancy is crucial for safety.
