An equal-tangent sag vertical curve is designed for 45 mi/h. The low point is 237 ft from the PVC at station 112 37 and the final offset at the PVT is 19.355 ft. If the PVC is at station 110 00, what is the elevation difference between the PVT and a point on the curve at station 111 00

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.