Question

The temperature in Boone, NC started -14 degrees C and rose 2 degrees every hour. The temperature in Monroe, NC started at -2 degrees C and rose 1 degree every 2 hours.



What will the temperature be when both cities have the same tempurature?

Answer 1

To solve for the time at which both cities have the same temperature, we can set up equations to represent the temperature in each city over time.

1. **Boone, NC**:
- Initial temperature: -14 degrees C
- Temperature increases by 2 degrees every hour.
- Therefore, the temperature \( T_B \) in Boone after \( t \) hours is given by:
\[
T_B = -14 + 2t
\]

2. **Monroe, NC**:
- Initial temperature: -2 degrees C
- Temperature increases by 1 degree every 2 hours, which is equivalent to 0.5 degrees every hour.
- Therefore, the temperature \( T_M \) in Monroe after \( t \) hours is given by:
\[
T_M = -2 + 0.5t
\]

To find when both temperatures are equal, we set the two equations equal to each other:
\[
-14 + 2t = -2 + 0.5t
\]

Now, we will solve for \( t \):
1. Rearrange the equation:
\[
2t - 0.5t = -2 + 14
\]
\[
1.5t = 12
\]

2. Divide both sides by 1.5:
\[
t = \frac{12}{1.5} = 8
\]

Now that we have \( t = 8 \) hours, we can find the temperature in either Boone or Monroe at this time:

**Boone's Temperature after 8 hours:**
\[
T_B = -14 + 2(8) = -14 + 16 = 2 \text{ degrees C}
\]

**Monroe's Temperature after 8 hours:**
\[
T_M = -2 + 0.5(8) = -2 + 4 = 2 \text{ degrees C}
\]

Both cities will have the same temperature of **2 degrees Celsius** after 8 hours.