In 60 minutes the minute hand moves 360 degrees, while the hour hand moves 30 degrees (5 mins=360/12=30). The minute hand moves 12 times faster than the hour hand. Let the angle of the minute hand from 12 o'clock be m degrees and the hour hand from 12 o'clock be h degrees. Starting with the hands showing 3 o'clock, we can write the equation m=12(h-90). When h=90 m=0, representing 3 o'clock. We want to find the next time the hands are exactly 90 degrees apart, so that's m-h=90. We have two equations and two variables. m=90+h, so we can write 90+h=12(h-90). So 90+h=12h-1080. 11h=1170, so h=106.3636... the next time the hands are at 90 degrees and m=196.3636... What time is this? Divide by 360 and multiply by 60 (therefore divide by 6 to convert degrees to clock minutes). t=m/6, where t is the time in minutes past the hour. The minutes are 32.7272... after the hour, so if we started at 3 o'clock the time would be 3:32.7272 or 3:32:44 approx. The minutes would be the same for other starting times, like 9 o'clock, for example.