Question

At the instant that a cake is removed from the oven, the temperature of the cake is 350°F. After 10 minutes, the cake's temperature is 200°F. If the temperature of the room is 70°F, how much longer will it take for the cake to cool to 90°F? (Round your answer to the nearest 5 minutes.)

a) 15 min
b) 20 min
c) 25 min
d) 30 min
e) 35 min
Please show your work. Thanks~

Answer 1

Once the cake is removed from the oven, it has been exposed to the room temperature of 70°F. After 10 minutes, the cake's temperature decreased to 200°F, which is 150°F cooler than it initially was (350°F). As for the what is asked, 90°F is 260°F cooler than its original temperature (350°F).

This problem can be expressed in a ratio:
10mins:150°F = N:260°F
where N is how long it will take for cake to cool to 90°F

150°FxN=10x260
150N=2600
N=2600/150
N=17.33
N≈20 minutes

Thus, it takes approximately 20 minutes for the cake to cool to 90°F