A clock has a minute hand with length 8 mm and an hour hand with length 4 mm, as shown below. The current time is one o’clock.

Find the rate at which the angle between the two hands is changing.

What is the first time after 1:00 at which the two hands will be exactly 90 degrees apart? Round to the nearest whole minute.

Rate of change of angle between hands

Time for 90 degree angle

Rate of change of angle between hands

Time for 90 degree angle

30 degrees per hour

Rate of change of angle between hands

Time for 90 degree angle

12 degrees per hour

Rate of change of angle between hands

Time for 90 degree angle

330 degrees per hour

Rate of change of angle between hands

Time for 90 degree angle

360 degrees per hour

Rate of change of angle between hands

Time for 90 degree angle

1:15

Rate of change of angle between hands

Time for 90 degree angle

1:20

Rate of change of angle between hands

Time for 90 degree angle

1:22

Rate of change of angle between hands

Time for 90 degree angle

1:25

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