1 at what time betweeen 7o'clock and 8o'clock will the hands of a watch be at right angles (for the first time)

Question

2 the floor of a room is in the form of a rectangle 'x'cm long and 'y'cm broad but with one corner rounded off by a quadrant of a circle of radius 'r' ,'r' bieng less than both x and y show that the area of the floor is given by A=xy-(1-22/7/4)r^2

Answer 1

1.) 7:15

Answer 2

Danny's answer is not correct, (just look at the angle at 7:15)
After 7:00 ....
When the minute hand has moved x°, the hour hand is at 210 + x/60

210 + x/60 - x = 90
12600 + x - 60x = 5400
-59x = -7200
x = 122.0338° or 20.34 minutes, 20 minutes + appr 20 seconds

so the time is 7:20:20