Question

Starting unheated, an electric stove oven takes 21 minutes and 44 seconds to reach a temperature of 350∘. Starting unheated, the oven takes 25 minutes and 19 seconds to reach a temperature of 400∘. The oven averages a.b seconds per degree in going from 350∘ to 400∘. What is a.b?

Answer 1

The oven needs 4.3 seconds to increase the temperature each °C. Thus

a=4, b=3

Explanation:

Linear Function

The relationship between two variables y and t is said to be linear if the increase of any amount in t always means the same increase in y. It's the same as saying that the rate of change of y with respect to t is constant.

The question provides the time t=21 minutes and 44 seconds it takes the electric stove oven to reach from unheated to 350°C.

The problem also says it takes 25 minutes and 19 seconds to reach from unheated to 400°C.

First, we compute both times in seconds:

t1=21*60+44=1304 seconds

t2=25*60+19=1519 seconds

It means the oven takes 1519 s - 1304 s = 215 seconds to reach from 350°C to 400°C.

We can know the average time it takes the oven to increase the temperature by one degree.

The average time can be computed as the ratio

`\displaystyle \bar t=(215\ s)/(400-350)=4.3\ s/^oC`

The oven needs 4.3 seconds to increase the temperature each °C. Thus

a=4, b=3