When you are taking a bath, how many kilograms of hot water at 480C must you mix with cold water at 120C so that the temperature of the bath is 360C? Assume the total mass of water (hot water + cold water) is 90kg.Question 11Answera.20 kgb.40 kgc.60 kgd.50 kg
Question
When you are taking a bath, how many kilograms of hot water at 480C must you mix with cold water at 120C so that the temperature of the bath is 360C? Assume the total mass of water (hot water + cold water) is 90kg.Question 11Answera.20 kgb.40 kgc.60 kgd.50 kg
Solution
The final temperature of the mixture is the weighted average of the initial temperatures of the hot and cold water. The weights are the masses of the hot and cold water.
Let's denote the mass of the hot water as m (in kg). The mass of the cold water is then 90 kg - m.
The equation for the final temperature is:
(m * Thot + (90 - m) * Tcold) / 90 = Tfinal
where: Thot is the initial temperature of the hot water, Tcold is the initial temperature of the cold water, and Tfinal is the final temperature of the mixture.
Substituting the given values into the equation, we get:
(m * 48°C + (90 - m) * 12°C) / 90 = 36°C
Solving this equation for m, we get:
m = (36°C * 90 - 12°C * 90) / (48°C - 12°C) = 60 kg.
So, you must mix 60 kg of hot water with the cold water to get a final temperature of 36°C. The correct answer is c. 60 kg.
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