Question

Suppose it is 40° inside your refrigerator and 340° inside your oven when the power goes out. The refrigerator temperature starts rising at the rate of 5° per hour. The oven temperature starts dropping at the rate of 45° per hour.

Answer 1

The temperature of both appliances is 70° after 6 hours.

At 6 hours, both temperatures will be equal

Explanation:

Equations

Let's call

T1 = Temperature inside of the refrigerator

T2 = Temperature inside of the oven.

x = Time in hours elapsed since the power goes out.

We know the temperature of the refrigerator rises at 5° per hour. Thus the function that models its temperature is:

T1 = 40 + 5x

We are also given the oven temperature drops by 45° per hour, thus:

T2 = 340 - 45x

a) Find the value of x for both temperatures to be the same.

We equal T1 and T2:

40 + 5x = 340 - 45x

Adding 45x

40 + 5x + 45x = 340

Subtracting 40:

5x + 45x = 340 - 40

Operating:

50x = 300

x = 300/50

x = 6

At 6 hours, both temperatures will be equal

b)

The common temperature can be found by substituting x in any function:

T1 = 40 + 5x = 40 + 5(6) = 40 + 30 = 70

T2 = 340 - 45x = 340 - 45(6) = 70

The temperature of both appliances is 70° after 6 hours.