The tip of a 1/4inch-long hour hand on a watch moves at a speed of 0.00000207 miles per hour. How far has it traveled in a day?

To find out how far the tip of the hour hand has traveled in a day, we need to determine the speed at which it moves in inches per day and then convert it to miles.

Step 1: Calculate the speed in inches per day.
The given speed is 0.00000207 miles per hour.
There are 24 hours in a day, so we need to multiply the given speed by 24 to find the speed in inches per day.
\text{Speed (inches per day)} = 0.00000207 \times 24

Step 2: Convert the speed to miles.
Since there are 12 inches in a foot and 5280 feet in a mile, we can convert the speed from inches to miles by dividing it by 12 and then by 5280.
\text{Speed (miles per day)} = \frac{{0.00000207 \times 24}}{{12 \times 5280}}

Step 3: Calculate the distance traveled in a day.
To find the distance traveled in a day, we need to multiply the speed in miles per day by the length of the hour hand, which is 1/4 inch.
\text{Distance traveled in a day} = \text{Speed (miles per day)} \times \text{length of hour hand}

Answer: Let's substitute the given values into the equation to find the answer.
\text{Distance traveled in a day} = \left(\frac{{0.00000207 \times 24}}{{12 \times 5280}}\right) \times \frac{1}{4}