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.
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website! 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.
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
(x1,y1) = (0,20) and (x2,y2) = (60,140),
Then find x when y = 50
  
So the slope is m = 2
Now we find the equation of the line by substituting
m = 2 and (x1,y1) = (0,20)
into the point-slope formula for the equation of a line:
Don't substitute
y - y1 = m(x - x1)
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
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