As the hour hand goes from 3 to 4 the minute hand will travel all the way around the clock so there must be a time between 3 and 4 when the two hands are at right angles. x minutes after 3, the minute hand will make an angle of (x/60)(360)= 6x degrees with the vertical. During that same time the hour hand will have moved a fraction x/60 of the angle between 3 and 4. Since there are 12 hour steps in 360 degrees the angle between 3 and 4 is 360/12= 30 degrees. The hour hand will have moved (x/60)(30)= x/2 degrees and so will be at 90+ x/2 degrees. The angle between the minute hand and the hour hand, x minutes after 3, is 6x- 90- x/2= (11/2)x- 90= 90. Solve that for x.