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Difficulty: HardUnit Conversions in Motion Problems

A naval submarine is traveling underwater at a constant speed of 20 feet per second20\text{ feet per second}. At this rate, how many miles will the submarine travel in exactly 1 hour1\text{ hour} and 6 minutes6\text{ minutes}?

(Note: 1 mile=5,280 feet1\text{ mile} = 5,280\text{ feet})

Answer: 15 miles

Answer

15
First, the rate is given as 20 feet per second. The total time must be converted entirely to seconds: 1 hour and 6 minutes equals 66 minutes. Multiplying 66 minutes by 60 seconds per minute gives 3,960 seconds. Next, use the formula Distance = Rate × Time to find the distance in feet: 20 × 3,960 = 79,200 feet. Finally, convert this distance into miles by dividing by 5,280. 79,200 ÷ 5,280 = 15 miles.

Step-by-Step Solution

1
Convert the total travel time into seconds to match the unit of the given speed.
The total time is 3,960 seconds.
Rates and times must share the same time unit before multiplying.
2
Calculate the total distance traveled in feet by multiplying the speed by the time in seconds.
The distance is 79,200 feet.
Distance equals rate multiplied by time (d = r * t).
3
Convert the distance from feet into miles by dividing by 5,280.
The final distance is 15 miles.
The question asks for the final answer in miles, and there are 5,280 feet in one mile.

Key Concept

Converting between multiple units of time and distance to solve for a missing variable in the distance formula.
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Topics

Unit Conversions in Motion Problems

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