Question

Temperature: The temperature in Coldspot is -7° and is increasing 2.5° per hour. The temperature in Frostberg is 19° and is decreasing 4° per hour. How long will it be until the temperatures are the same? Write and solve an equation the represents the scenario.

Answer 1

Answer:

It will be 4 hours until the temperatures are the same

Step-by-step explanation:

Let $T_{c}$ represent the temperature in Coldspot in $x$ hours and

$T_{f}$ represent the temperature in Frostberg in $x$ hours.

From the question,

The temperature in Coldspot is -7° and is increasing 2.5° per hour, then we can write that

$T_{c} = -7 + 2.5x$

Also, from the question,

The temperature in Frostberg is 19° and is decreasing 4° per hour, then we can write that

$T_{f} = 19 - 4x$

To determine how long it will be until the temperatures are the same, that is when $T_{c}$ will be equal to $T_{f}$, we will equate the two equations and determine $x$.

$x$ will give the number of hours until the temperatures are the same.

$T_{c} = T_{f}$

$-7 + 2.5x = 19 - 4x$

Then,

$4x + 2.5x = 19 + 7$

$6.5x = 26$

$x = \frac{26}{6.5}$

∴ $x = 4$

Hence, it will be 4 hours until the temperatures are the same.