Dana rode her bicycle 600 miles one summer before she had to replace the tire on her front wheel. The diameter of the front wheel is 24 inches. What is the best estimate of the number of revolutions made by the tire before it had to be replaced?

you know the circumference of the tire is 24pi or 75.4 inches.

So, figure out how many inches there are in 600 miles, and divide that by 75.4

That's how many times the tire went around.

I need to convert this correct. I think that's my biggest issue. Since the diameter is in inches and the distance is in miles, wouldn't I have to convert the miles into inches?

well, yes, as I said. So, just work it out:

600 mi * 5280ft/mi * 12in/ft = 38,016,000 in

Note how the units cancel, leaving you with just inches.

Sorry. I think I was reading too fast and missed that. Thank you.

To find the number of revolutions made by the tire, we need to know the circumference of the tire and divide the total distance covered by it.

The circumference of a circle can be calculated using the formula: Circumference = π * diameter.

Given that the diameter of Dana's front wheel is 24 inches, we can calculate its circumference as follows:
Circumference = π * 24 inches.

Since we are looking for an estimate, we can use π as approximately 3.14:
Circumference ≈ 3.14 * 24 inches.

Next, we need to convert the total distance Dana rode into the number of revolutions. Since the circumference of the tire represents the distance covered in one revolution, we can divide the total distance by the circumference.

Number of revolutions = Total distance covered / Circumference.

Given that Dana rode 600 miles, we need to convert this distance into inches to match the units of the circumference (in inches):
Total distance covered = 600 miles * 5280 feet/mile * 12 inches/foot.

Now, we can substitute the values into the formula to get the best estimate of the number of revolutions made by the tire:
Number of revolutions ≈ (600 miles * 5280 feet/mile * 12 inches/foot) / (3.14 * 24 inches).

By performing the calculation, we will get the best estimate of the number of revolutions made by the tire before replacement.