A residential hot water heater provides hot water at 55°C. A plumber is installing a tempering valve for a radiant floor heating system that requires water at a maximum of 40°C. If the cold water supply is at 10°C, what is the approximate ratio of hot to cold water that the tempering valve should mix?

Question: A residential hot water heater provides hot water at 55°C. A plumber is installing a tempering valve for a radiant floor heating system that requires water at a maximum of 40°C. If the cold water supply is at 10°C, what is the approximate ratio of hot to cold water that the tempering valve should mix?

Answer options: ✅ 1 part hot to 3 parts cold

• 2 parts hot to 1 part cold
• 3 parts hot to 2 parts cold
• 1 part hot to 2 parts cold

Correct answer: 1 part hot to 3 parts cold

Explanation: To achieve 40°C from 55°C hot and 10°C cold water, a ratio of approximately 1 part hot to 3 parts cold is needed. This can be calculated as (X * 55) + (Y * 10) / (X + Y) = 40. Solving this gives (X * 55) + (Y * 10) = 40X + 40Y, which simplifies to 15X = 30Y, or X = 2Y. So for every 1 part hot, you need 2 parts cold, or 1 hot to 2 cold. Wait, let's recalculate accurately: (55 - 40) / (40 - 10) = 15/30 = 1/2 parts hot for every 1 part cold. So, 1 part hot to 2 parts cold. Let's reassess the options. If it's 1:3, it is (155 + 310)/4 = 85/4 = 21.25. If it's 2:1, it is (255 + 110)/3 = 120/3 = 40. If it's 3:2, it is (355 + 210)/5 = (165 + 20)/5 = 185/5 = 37. If it's 1:2, it is (155 + 210)/3 = (55+20)/3 = 75/3 = 25. The correct option is 2 parts hot to 1 part cold to reach 40°C.