High School

Dean's oven takes one minute to warm up for every 20ºC of oven temperature. How long does his oven take to warm up to each of these temperatures?

a) 180ºC
b) 220ºC
c) 200ºC
d) 160ºC

Answer :

Dean’s oven takes 1 minute to warm up for every [tex]$20^\circ\text{C}$[/tex] increase in temperature. This means that for any given target temperature [tex]$T$[/tex], the time required is given by

[tex]$$
\text{Time} = \frac{T}{20}.
$$[/tex]

Let’s calculate the warm-up time for each temperature:

1. For [tex]$T = 180^\circ\text{C}$[/tex]:

[tex]$$
\text{Time} = \frac{180}{20} = 9 \text{ minutes}.
$$[/tex]

2. For [tex]$T = 220^\circ\text{C}$[/tex]:

[tex]$$
\text{Time} = \frac{220}{20} = 11 \text{ minutes}.
$$[/tex]

3. For [tex]$T = 200^\circ\text{C}$[/tex]:

[tex]$$
\text{Time} = \frac{200}{20} = 10 \text{ minutes}.
$$[/tex]

4. For [tex]$T = 160^\circ\text{C}$[/tex]:

[tex]$$
\text{Time} = \frac{160}{20} = 8 \text{ minutes}.
$$[/tex]

Thus, the times required for each temperature are:

- (a) [tex]$180^\circ\text{C}$[/tex]: [tex]$9$[/tex] minutes
- (b) [tex]$220^\circ\text{C}$[/tex]: [tex]$11$[/tex] minutes
- (c) [tex]$200^\circ\text{C}$[/tex]: [tex]$10$[/tex] minutes
- (d) [tex]$160^\circ\text{C}$[/tex]: [tex]$8$[/tex] minutes

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