Question

a meteorologist recorded the temperatures at two weather stations. at noon, the temperature at station a was 43 degrees fahrenheit, and it decreased at a constant rate of 5 degrees per hour over the course of the day. at noon, the temperature at station b was -6 degrees fahrenheit, and increased at a constant rate of 2 degrees per hour. after how many hours will the two stations have exactly the same temperature?
we can use a table below to record the temperatures at each station after given times. the first row has been completed for you: we can think of the temperatures at noon as 0 hours since that’s our starting temperature. use the expressions for each station to find their temperatures after each of these times. you can use the calculator to help you solve.
station a’s temperature after ( t ) hours: ( 43 + (-5t) )
station b’s temperature after ( t ) hours: ( -6 + 2t )

hours	0	3	6	9
station b’s temperature	-6	( square )	( square )	( square )

Explanation:

Step1: Fill Station A at t=3

Substitute t=3 into $43 + (-5t)$
$43 + (-5\times3) = 43 - 15 = 28$

Step2: Fill Station A at t=6

Substitute t=6 into $43 + (-5t)$
$43 + (-5\times6) = 43 - 30 = 13$

Step3: Fill Station A at t=9

Substitute t=9 into $43 + (-5t)$
$43 + (-5\times9) = 43 - 45 = -2$

Step4: Fill Station B at t=3

Substitute t=3 into $-6 + 2t$
$-6 + (2\times3) = -6 + 6 = 0$

Step5: Fill Station B at t=6

Substitute t=6 into $-6 + 2t$
$-6 + (2\times6) = -6 + 12 = 6$

Step6: Fill Station B at t=9

Substitute t=9 into $-6 + 2t$
$-6 + (2\times9) = -6 + 18 = 12$

Step7: Find equal temp time

Set expressions equal: $43 -5t = -6 +2t$

Step8: Rearrange to solve for t

$43 +6 = 2t +5t$
$49 =7t$
$t=\frac{49}{7}=7$

Answer:

Completed Table:

Hours	Station A's temperature	Station B's temperature
3	28	0
6	13	6
9	-2	12

Time for equal temperature:

7 hours