Question

The temperature is 60°F. The temperature will decrease by 3°F each hours. Let h be the number of hours. When will the temperature be below 32° F? Write an inequality for this problem.

Answer 1

For the temperature to be below 32 F, following inequality must be met,

`h\geq 9.333`

Explanation:

Let "t" be the temperature at any time.

General format of a linear equation can be given as,

y= mx + c

Where,

y ⇒ dependent variable ( in this case temperature t)

m⇒ Gradient ( the rate at which the temperature drops)

x⇒ independent variable ( hours )

c⇒ intercept ( this is the starting temperature)

Now we can substitute the given values to the above format to arrive at the equation,

`t=-3h+60`

We can re-arrange the equations as ,

`3h=60-t`

=
`h=20-(t)/(3)`

We can write this as an inequality when t = 32 F

`h\geq 20-(32)/(3)`

=
`h\geq (28)/(3)`

=
`h\geq 9.333`