### Brain Teasers

# Water Temps

Pretend you have two faucets for your shower, one that releases hot water and one that releases cold water, but at varying pressures. If the hot water is 105 degrees Fahrenheit and the cold water is 45 degrees Fahrenheit, and you could rotate the faucet at most 360 degrees, how much would you have to rotate the cold water faucet to get the temperature to be 98.6 degrees Fahrenheit, if the hot water is turned on all the way, and could not be turned down?

### Hint

Add how much you've rotated each and divide by the total rotation to get the average temperature.### Answer

the equation for finding the answer, explained by the hint, is (105(360)+(45)(x))/(360+x)=98.6Solving for x:

x= 42.985 degrees

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## Comments

This was a good puzzle, I think you missed the follow up question though, Which would be.... How many degrees would you have to increase the cold water knob if there was a 10% loss in water preasure because your roomate thought it would be funny to flush the toilet. And then the subsequent volumn question of the timely filling of the tub for holding his head under.

Pfft! Hot water flow will drop as cold water flow increases. even without flushing a toilet. Faucets are not linear in their function. Some will deliver full force at less than full rotation. Some will increase flow much less than 10% during last 10% of functional rotation.

Excellent puzzle. I confused myself by thinking about the zero case and the full on case and then working on averages but of course at the extreme ends you don't have to worry about the volume of water flowing from the cold tap. After I read the hint I realised that I could not just work off the two extremities.

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