Question 998454
A potato at room temperature of 20°C is placed in an oven whose 
temperature is 200°C. An hour later the temperature of a potato 
is 140°C. Under the (unreasonable) assumption that the potato's 
temperature is always uniform, how long did it take the potato 
to reach 50°C.
<pre>
You can do this in your head because if it takes an hour for
the potato to heat up from 20° to 140°, which is an increase 
of 120°, then to heat up from 20° to only 50°, an increase of 30°
which happens to be 1/4 of 120°, it will obviously take it only
1/4 as long or 1/4 of an hour or 15 minutes.

But here is how to do it using algebra:

When time = 0 minutes, the temperature of potato is 20°
when time = 60 minutes, the temperature of the potato is 140°
When time = ? minutes, the temperature of the potato is 50°.

This problem reduces to:

Find the equation of the line through the points 

(x<sub>1</sub>,y<sub>1</sub>) = (0,20) and (x<sub>2</sub>,y<sub>2</sub>) = (60,140),

Then find x when y = 50

{{{m}}}{{{""=""}}}{{{(y[2]-y[1])/(x[2]-x[1])}}} 

{{{m}}}{{{""=""}}}{{{(140-20)/(60-0)}}}

{{{m}}}{{{""=""}}}{{{120/60}}}

{{{m}}}{{{""=""}}}{{{2}}}

So the slope is m = 2

Now we find the equation of the line by substituting 

m = 2 and (x<sub>1</sub>,y<sub>1</sub>) = (0,20)

into the point-slope formula for the equation of a line:

Don't substitute 

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

y - 20 = 2(x - 0)

y - 20 = 2x

     y = 2x + 20

Now we want to find x when y = 50
So we substitute 50 for y and solve for x:

    50 = 2x + 20
    30 = 2x
    15 = x

So it will take 15 minutes.

Edwin</pre>