Question

The inside wheels of a car traveling on a circular path are rotating half as fast as the outside wheels. The front two wheels are six feet apart. What is the number of feet in the path traced by the inside front wheel in one trip around the circle? Express your answer in the form "k \pi", where k is an integer.

Answer 1

The total path traced by the inside front wheel in one trip around the circle = k·π , where k = 12 is an integer

Explanation:

To find the distance traced by the wheel around the circle, we need to find the circumference which is given by : 2π·r

Now, let radius of inside wheel be r feet

⇒ radius of outside wheel = (r + 6) because the inside wheel is 6 feet apart from the outside wheel.

Now, the inside wheels are rotating at half speed as compared to that of outside wheels.

⇒ 2×Circumference of inside wheel = Circumference of outside wheel

⇒ 2×(2π·r) = 2π × (r+6)

⇒ 2π· r = π· r + 6·π

⇒ π·r = 6·π

⇒ r = 6

Hence, the total path traced by the inside front wheel in one trip around the circle = 2π·r

= 2π × 6

= 12·π

= k·π , where k = 12 is an integer