Submarine $A$ is positioned at -1,100 feet in relation to sea level. Submarine $B$ is positioned at -800 feet in relation to sea level. Each submarine needs to be 200 feet below sea level in 30 minutes. Which compares the speeds at which each submarine needs to travel?
A. Submarine A must travel at a rate of $\frac{-200-(-1100)}{30}=30 ft / min$, and Submarine B must travel at a rate of $\frac{-200-(-800)}{30}-20 ftmin$.
B. Submarine A must travel at a rate of $\frac{1100+200}{30}=43 \frac{1}{3} ft / min$, and Submarine B must travel at a rate of $\frac{800+200}{30}=33 \frac{1}{3} ft / min$.
C. Submarine A must travel at a rate of $\frac{-1100}{30}=-36 \frac{2}{3} ft / min$, and Submarine B must travel at a rate of $\frac{-800}{30}=-26 \frac{2}{3} fv / min$.
Answer (2)
Calculate the distance Submarine A needs to travel: d i s t an c e A = − 200 − ( − 1100 ) = 900 feet.
Calculate the speed Submarine A needs to travel: s p ee d A = 30 900 = 30 feet per minute.
Calculate the distance Submarine B needs to travel: d i s t an c e B = − 200 − ( − 800 ) = 600 feet.
Calculate the speed Submarine B needs to travel: s p ee d B = 30 600 = 20 feet per minute. Therefore, Submarine A must travel faster than Submarine B. s p ee d A = 30 f t / min , s p ee d B = 20 f t / min
Explanation
Problem Analysis Let's analyze the problem. We have two submarines, A and B, at different depths. We need to find the speeds at which they must travel to reach a depth of -200 feet in 30 minutes.
Distance Calculation for Submarine A First, we need to calculate the distance each submarine needs to travel. Submarine A starts at -1100 feet and needs to reach -200 feet. The distance it needs to travel is the difference between these two positions: d i s t an c e A = − 200 − ( − 1100 ) .
Simplifying Distance A Simplifying the expression, we get d i s t an c e A = − 200 + 1100 = 900 feet.
Speed Calculation for Submarine A Now, we calculate the speed Submarine A needs to travel. Since it needs to cover 900 feet in 30 minutes, its speed is s p ee d A = 30 900 = 30 feet per minute.
Distance Calculation for Submarine B Next, we calculate the distance Submarine B needs to travel. Submarine B starts at -800 feet and needs to reach -200 feet. The distance it needs to travel is the difference between these two positions: d i s t an c e B = − 200 − ( − 800 ) .
Simplifying Distance B Simplifying the expression, we get d i s t an c e B = − 200 + 800 = 600 feet.
Speed Calculation for Submarine B Now, we calculate the speed Submarine B needs to travel. Since it needs to cover 600 feet in 30 minutes, its speed is s p ee d B = 30 600 = 20 feet per minute.
Comparing Speeds Finally, we compare the speeds. Submarine A needs to travel at 30 feet per minute, and Submarine B needs to travel at 20 feet per minute. Therefore, Submarine A must travel faster than Submarine B.
Examples
Imagine you're controlling two drones underwater, each at a different depth, and you need to bring them both to a specific level within a set time. This problem helps you calculate how fast each drone needs to move to reach the target depth on time. Understanding these calculations is crucial for coordinating underwater missions, ensuring that all equipment arrives at the designated location simultaneously and efficiently. This type of problem applies to various real-world scenarios, such as search and rescue operations, marine research, and underwater construction.
Submarine A must travel at 30 ft/min, while Submarine B needs to travel at 20 ft/min to reach -200 feet in 30 minutes. Therefore, Submarine A travels faster than Submarine B. The calculations show that Submarine A has a greater required speed than Submarine B.
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