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.
waec 1995physics

The correct answer is A. 90oC

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

\(\therefore 50 = \frac{b(t) + 2b(30)}{b + 2b}\)

\(50 = \frac{bt + 2b(30)}{3b}\)

\(50(3b) = bt + 2b(30) \implies 150b = b(t + 60)\)

\(150 = t + 60 \implies t = 150 - 60 = 90°C\)

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