# Algebra

posted by .

At what time between 7 and 8 on an analog clock do the hour and minute hand overlap?

• Algebra -

At 7:00 the hour hand has gone through 210° , and angle between the two hands is 210°

the hour hand moves 30° per hour or 1/2 ° per minute
while the minute hand moves 6 degrees per minute
so the minute is gaining on the hour hand at the rate of 5 1/2 or 11/2 ° a minute
So to make up the 210° would take 210÷(11/2)
= 420/11 minutes or 38 2/11 minutes or 38 : 10.9 minutes

so the time is 7 : 38 : 10.9

The above becomes a general solution;
at any time between t and t+1 o'clock,
divide t by 11/2 to find the minutes past t o'clock when the hands overlap

## Similar Questions

1. ### Math

As the time changes from 4:10 pm to 6:45 pm on the analog clock, determine the change in radian measure of the minute hand.
2. ### Math Trig

As the time changes from 4:10 pm to 6:45 pm on the analog clock, determine the change in radian measure of the minute hand.
3. ### physics

When it is 10:00, the hour hand on an analog clock is 300 degrees ahead of the minute hand. How many minutes elapse (to three significant digits) before the minute hand next points in the same direction as the hour hand?
4. ### physics

At 15 minutes past the hour, a 50 g mouse runs up a grandfather clock and sits himself down at the end of the minute-hand. If the minute-hand for the clock is 16 cm long, what is the magnitude of the torque exerted by the mouse on …
5. ### trigonometry

a clock has a dial face of 12 inches radius the minute hand is 9 inches while the hour hand is 6 inches the plane of rotation of the hour hand is 2 inches above the plane of rotation of the minute hand. Find the distance between the …
6. ### math

A grandfather clock shows a time of 7 o’clock. What is the exact radian measure of the angle between the hour hand and the minute hand?
7. ### matha

the minute hand of a clock is 9m long. the hour hand clock is 2/3 times longer than the minute clock. how much more distance will minute hand clock more than hour clock in 1 hour/
8. ### maths

the minute hand of a clock is 9cm long. the hour hand clock is 2/3 times longer than the minute clock. how much more distance will minute hand clock move than hour clock in 1 hour?
9. ### Calculus

If a valid time on a 12 hour time period has the hour hand and minute hand switched, how many times will that result in another valid time?
10. ### Algebra 2

Neela's clock is broken the minute hand rotates around the clock correctly but the hour hand is stuck in the three o'clock position. Suppose neela first looks at the clock when the hands are aligned and it shows 3:15. She looks at …

More Similar Questions