Schematic Diagram of the circuit
The way the circuit is drawn does not match the wording of the question, so my answer assumes the wording is correct and the circuit switch is wrong as that makes more logical sense from a learning circuits standpoint.

When on, the resistors R1 and R3 act as series equivalent resistors and are therefore just summed together. If the switch is closed long enough, the capacitor will be charged to Vt. When in the off position, where R3 and R2 are now connected, they will discharge the capacitor through the new equivalent series resistor which may also be summed together to find the equivalent resistance.