Systems of linear equations

Question

The temperature changes of 2 calorimeters were monitored and recorded. Calorimeter A contain 250 mL of water with an initial water temperature of 120°F. After 10 minutes the temperature of the water in Calorimeter A steadily decreased to 100°F. Calorimeter B contained the same amount of water as Calorimeter A but it's initial water temperature was 20°F. The rate of increase in water temperature in Calorimeter B was 3°F per minute. Write a system of linear equations for the temperature, T°F, of the water in calorimeters A and B in terms of the time ,minutes

Answer 1

You said for A that the temperature started as "one 20°F".  I assume you meant 120°F.  Please edit the question.  Anyway, here is a solution based on 120°F.

 

Calorimeter A:

 

T_A(t) = kt + T₀

 

T₀ = 120°F

 

k = rate of temperature change = (100°F - 120ºF) / (10 min) = -2°F/min

 

Final equation:

 

T_A(t) = -2t + 120, with t in minutes, T_A in °F.

 

Calorimeter B:

 

Solve in a similar way.  You are given k_B = 3°F/min

 

T_0B = 20°F

 

T_B(t) = 3t + 20, with t in minutes and T_B in °F