Question

The temperature in Acton is 65°F and rising by 3°F each hour. The temperature in Tempe, Arizona, is 105°F and falling by 2°F each hour. After how many hours will the temperature in Acton and Tempe be the same?

a) 35 hours
b) 40 hours
c) 45 hours
d) 50 hours

Answer 1

To determine when the temperatures in Acton and Tempe will be the same, we set up an equation based on their starting temperatures and their rates of change. Solving the equation indicates that after 8 hours the temperatures will be the same. The provided multiple choice options do not include the correct answer.

Step-by-step explanation:

To find out after how many hours the temperatures in Acton and Tempe will be the same, we can set up an equation to represent the changing temperatures. Let's let x represent the number of hours it takes for the temperatures to be equal.

For Acton, the temperature starts at 65°F and increases by 3°F each hour. So the temperature in Acton after x hours is 65 + 3x degrees Fahrenheit.

For Tempe, the temperature starts at 105°F and decreases by 2°F each hour. So the temperature in Tempe after x hours is 105 - 2x degrees Fahrenheit.

Setting these two expressions equal to each other because we're looking for when the temperatures are the same, we get:
65 + 3x = 105 - 2x.

Now solve for x:

1. Add 2x to both sides of the equation, which gives us: 65 + 5x = 105.
2. Subtract 65 from both sides, resulting in 5x = 40.
3. Divide both sides by 5, yielding x = 8.

So after 8 hours, the temperature in Acton will equal the temperature in Tempe. None of the multiple choice options provided (a) 35 hours, (b) 40 hours, (c) 45 hours, (d) 50 hours correspond to the correct answer which is 8 hours. There might have been a mistake in the options provided.