At exactly what time past 4:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
Choose the correct choice from the following:
A) 20 13/21 minutes past 7:00 B) 20 13/17 minutes past 7:00 C) 21 3/23 minutes past 7:00 D) 21 9/11 minutes past 4:00 E) 22 4/9 minutes past 7:00
5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?   That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 4:00. At 4:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.   So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of   210-90= 
<gadget id="calculator">  210-90</gadget>
<output>120</output>
120 degree at the rate of 5.5 degrees per minute ---&gt; 120/5.5= 21 9/11 minutes.   Thus, 21 9/11 minutes past 4:00 is the correct answer.
<result>D</result>
At exactly what time past 4:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?