Hot water at a temperature of t is added to twice that amount of water at a temperature of 30°C. If the resulting temperature of the mixture is 50°C. Calculate t.
-
A.
90oC -
B.
80oC -
C.
50oC -
D.
40oC -
E.
30oC.
Correct Answer: Option A
Explanation
Final Temperature = (frac{m_1 T_1 + m_2 T_2}{m_1 + m_2})
where m(_1) and m(_2) are the weights of the water in the first and second containers.
T(_1) and T(_2) are the temperatures of the water in the first and second container.
Given Final temperature = 50°C;
Let m(_1) = b, then m(_2) = 2b.
T(_1) = t; T(_2) = 30°C
(therefore 50 = frac{b(t) + 2b(30)}{b + 2b})
(50 = frac{bt + 2b(30)}{3b})
(50(3b) = bt + 2b(30) implies 150b = b(t + 60))
(150 = t + 60 implies t = 150 – 60 = 90°C)