Charging time of capacitor when used with this transistor configuration?
With the PUT being off and Q1 operating in linear mode, the capacitor is charged with a constant current. We know that: Ic = C * dv/dt . Ic is constant and has to be calculated. So the equation reduced to (V2 - V1)/T = Ic/C in which V2 is the voltage value of cap, V1 is the initial value and T is the time of charging and has to be calculated: 
Vb(Q1) = 20/25 * 15 = 12 
V(R4k) = (15-12-0.7), V(R4k)/4 = 0.575mA = Ic 
(10.7 - 0)/T = 0.575 / 1uF  find T ... 
T = 18.6 ms