In Peter’s home bathroom, there was a standard shower stall with everything working in a conventional fashion. Then Peter used some simple plumbing tools, and some ordinary, low-cost plumbing parts to make a modification. The next day, Peter took a shower first while Pam waited her turn. Peter finished and said, “Enjoy the shower, Pam!” She found both shower faucets in the off position. Then she turned on only the hot water faucet, and the water coming out the shower head alternated every 1 second, from hot to cold to hot. After 3 seconds, she shut off the hot water faucet and turned on only the cold water faucet, and the water coming out the shower head alternated every 1 second, from cold to hot to cold. After 3 seconds, she turned off the cold water faucet and shouted out, “Peter, what did you do?!”
What did Peter do to cause the water temperature to alternate?
Peter made no changes to the tank water heater, the faucets, or the shower head, which are all still working in a conventional fashion. Water still flows one-way only through all of the pipes. The only means of providing hot water to the shower head is from the tank water heater. The only means for providing cold water to the shower head is from the water main (or from a depleted tank water heater or while waiting for the hot water to reach the shower head). The supply from the water main is of constant temperature and pressure. Nobody but Pam touched the plumbing system after Peter told her to enjoy the shower.
Update / Hint
Draw a simplified plumbing schematic of a standard shower stall, and the solution should be easier to find. Below is such a drawing.