Final answer:
To find the temperature at noon, we calculated the rate of temperature increase from 10 A.M. to 3 P.M. and applied it for 2 hours from 10 A.M. The result is 43°F, which is option 2.
Step-by-step explanation:
The question involves determining the temperature at noon given that the temperature was 37°F at 10 A.M. and 52°F at 3 P.M., with a constant rate of increase. To calculate this, we first find the total increase in temperature from 10 A.M. to 3 P.M., which is 52°F - 37°F = 15°F. Next, we calculate the number of hours during which this increase occurred, which is 3 P.M. - 10 A.M. = 5 hours. Now, we can find the hourly rate of temperature increase by dividing the total increase by the number of hours, leading to an increase of 15°F / 5 hours = 3°F per hour.
Now, since noon is 2 hours after 10 A.M., we will multiply the hourly rate by 2 to find the increase by noon, which gives us 3°F per hour x 2 hours = 6°F. Finally, we add this increase to the temperature at 10 A.M. to find the temperature at noon: 37°F + 6°F = 43°F. Therefore, the temperature at noon was 43°F, which corresponds to option 2.