Answer:
Explanation:
To solve this problem, we can use the fact that the distance traveled by each wheel is proportional to its circumference, and the circumference of a circle is given by:
circumference = π x diameter
Using this formula, we can find the distance traveled by each wheel in one rotation, and then divide the total distance traveled by each wheel to find how many rotations each wheel made.
For the front wheels with a diameter of 35 inches, the circumference is:
circumference = π x 35
circumference ≈ 109.96 inches
In one mile, there are 5280 feet and 12 inches in a foot, so the distance traveled in one mile is:
distance in one mile = 5280 x 12 = 63360 inches
Therefore, the number of rotations made by the front wheels in one mile is:
rotations per mile = distance in one mile / circumference
rotations per mile ≈ 63360 / 109.96 ≈ 576.15
In 14 miles, the number of rotations made by the front wheels is:
rotations for front wheels = rotations per mile x 14
rotations for front wheels ≈ 576.15 x 14 ≈ 8066.10
For the rear wheels with a diameter of 56 inches, the circumference is:
circumference = π x 56
circumference ≈ 175.93 inches
Using the same calculation, the number of rotations made by the rear wheels in 14 miles is:
rotations for rear wheels = (distance in one mile / circumference) x 14
rotations for rear wheels ≈ (63360 / 175.93) x 14 ≈ 5068.21
The difference in the number of rotations made by the front wheels and the rear wheels is:
difference = rotations for front wheels - rotations for rear wheels
difference ≈ 8066.10 - 5068.21 ≈ 2997.89
Rounding the difference to the nearest whole number, we get:
difference ≈ 2998
Therefore, the front wheel rotated approximately 2998 more times than the rear wheel on this day.