# A weather forecaster predicts that the temperature in Antarctica will decrease 8^{circ}F each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36^{circ}F

A weather forecaster predicts that the temperature in Antarctica will decrease ${8}^{\circ }F$ each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least ${36}^{\circ }F$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Given information:
Since, the temperature in Antarctica decreases by ${8}^{\circ }F$ each hour for every 6 hours, using h as the number of hours it will take to drop at least ${36}^{\circ }F$, then we can use the inequality $8h\ge 36$:
Calculation:
Given,
$8h\ge 36$
Divide both sides of the inequality by 8
$\frac{8h}{8}\ge \frac{36}{8}$
$h\ge 4.5$
Hence, the minimum hours it will take at least 4.5 hours before the temperature drops to ${36}^{\circ }F.$
###### Not exactly what you’re looking for?
Jeffrey Jordon

Given:
m = -8 degrees/hour, the rate of change of temperature

Let x =  hours
Let y = temperature, ${}^{\circ }F$
Then y = -8x + b
where b = constant

When x = 0, then y = b.
Therefore b = initial temperature

If the temperature drops by at least 36 ${}^{\circ }F$ in the next x hours, then
$b-y\left(6\right)\ge 36$
$b-\left(-8x+b\right)\ge 36$
$8x\ge 36$