A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her stay at the factory. For how long did she stay in the factory?
7.5 hours
Understanding Clock Hand Movement
To determine how long the worker stayed at the factory, we need to understand how the hour hand of a clock moves. A standard clock face is a circle, which measures 360 degrees.
- The hour hand completes a full circle (360 degrees) in 12 hours.
- This means that in 1 hour, the hour hand moves a certain number of degrees.
We can calculate the speed of the hour hand in degrees per hour:
Speed of hour hand = $\frac{360 \text{ degrees}}{12 \text{ hours}}$
Speed of hour hand = $30 \text{ degrees per hour}$
Calculating Time Duration
The worker noticed that the hour hand moved by 225 degrees. We know the speed of the hour hand is 30 degrees per hour. To find out how long she stayed, we divide the total degrees moved by the speed of the hour hand.
Duration of stay = $\frac{\text{Total degrees moved by hour hand}}{\text{Speed of hour hand}}$
Duration of stay = $\frac{225 \text{ degrees}}{30 \text{ degrees per hour}}$
Let's perform the division:
Duration of stay = $7.5 \text{ hours}$
Final Time Spent
The calculation shows that the worker stayed for 7.5 hours. This can also be expressed as 7 hours and 30 minutes, as 0.5 hours is half of an hour, which is 30 minutes.
| Clock Hand | Movement in 1 Hour |
|---|---|
| Hour Hand | 30 degrees |
| Minute Hand | 360 degrees |
Therefore, if the hour hand moved by 225 degrees, the worker's stay at the factory was 7.5 hours.
Important Questions from Numerical Computation
Ratio of the angles of a triangle are 1 : 2 : 6. What is the smallest angle?
It would take one machine 4 hours to complete a production order and another machine 2 hour to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours.
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_remaining in the budget.
What is the value of \(1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + \frac{1}{{256}} + \ldots ?\)
A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?
