Question

A restaurant occupying the top floor of a skyscraper rotates as diners enjoy the view. Ling and Sarah notice that they began their meal at $7 : 00$ P.M. looking due north. At $7 : 45$ P.M. they had rotated $180^{\circ}$ to a view that was due south. At this rate, how many degrees will the restaurant rotate in 1 hour? A. $180^{\circ}$ C. $240^{\circ}$ D. $270^{\circ}$ E. $400^{\circ}$

Name: Problem 1, Chapter :
Uploaded: 2021-06-14T23:29:12-08:00
Duration: 1 min 26 s
Channel: Dharmendra Jain
Description: A restaurant occupying the top floor of a skyscraper rotates as diners enjoy the view. Ling and Sarah notice that they began their meal at 7 : 00 P.M. looking due north. At 7 : 45 P.M. they had rotated 180^∘ to a view that was due south. At this rate, how many degrees will the restaurant rotate in 1 hour? A. 180^∘ C. 240^∘ D. 270^∘ E. 400^∘

   A restaurant occupying the top floor of a skyscraper rotates as diners enjoy the view. Ling and Sarah notice that they began their meal at $7 : 00$ P.M. looking due north. At $7 : 45$ P.M. they had rotated $180^{\circ}$ to a view that was due south. At this rate, how many degrees will the restaurant rotate in 1 hour?
A. $180^{\circ}$
C. $240^{\circ}$
D. $270^{\circ}$
E. $400^{\circ}$

Instant Answer

Solved by Expert Dharmendra Jain

06/14/2021

Step 1

Since they started at 7:00 PM and reached 180 degrees at 7:45 PM, it took 45 minutes for the rotation. Now, we want to find out how many degrees the restaurant will rotate in 1 hour (60 minutes). To do this, we can set up a proportion: $\frac{180^{\circ}}{45 Show more…

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A restaurant occupying the top floor of a skyscraper rotates as diners enjoy the view. Ling and Sarah notice that they began their meal at $7 : 00$ P.M. looking due north. At $7 : 45$ P.M. they had rotated $180^{\circ}$ to a view that was due south. At this rate, how many degrees will the restaurant rotate in 1 hour? A. $180^{\circ}$ C. $240^{\circ}$ D. $270^{\circ}$ E. $400^{\circ}$

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Key Concepts

Rate Calculation

Rate calculation involves determining how much rotation occurs over a given time period. In problems like this, computing the degrees rotated per minute or hour allows one to extrapolate the rotation over different time intervals by applying basic arithmetic operations like multiplication or division.

Angular Rotation

Angular rotation refers to the measure of how much an object has turned about a fixed point or axis. In contexts like rotating restaurants, it describes the degree of rotation over time and is essential for determining how far the restaurant rotates as it moves through specific angles.

Proportional Reasoning

Proportional reasoning is the process of relating two quantities that change at a constant rate, such as degrees rotated and time elapsed. This concept is used to scale known rotations to find unknown rotations over different time intervals, ensuring that the relationship between the quantities remains consistent.

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