A tank supplies water at 30°C, while another supplies water at 86°C. If a man wishes to bathe with water at 44°C, calculate the ratio of the mass of hot water to that of the cold needed.

To find the ratio of the mass of hot water to that of the cold water needed, we can use the principle of conservation of energy.

Let the mass of hot water be m1 and the mass of cold water be m2. The specific heat capacity of water is 4.18 J/g°C.

The heat lost by the hot water = heat gained by the cold water

m1 * 4.18 * (86 - 44) = m2 * 4.18 * (44 - 30)

m1 * 4.18 * 42 = m2 * 4.18 * 14

m1/m2 = 14/42

m1/m2 = 1/3

Therefore, the ratio of the mass of hot water to that of the cold water needed is 1:3.

Let the mass of hot water be m1 and the mass of cold water be m2.

Heat gained by cold water = m2 - 4190 - (44 - 30) J

Heat lost by hot water = m1 - 4190 - (86 - 44) J

Since the heat gained by cold water is equal to the heat lost by hot water, we have:

m2 - 4190 - (44 - 30) = m1 - 4190 - (86 - 44)

Simplifying the equation, we get:

m2 - 14 = m1 - 42

Dividing both sides by m1, we get:

m2/m1 = 3

Therefore, the ratio of the mass of hot water to that of the cold needed is 3:1.

I:3 is the answer