How many rotations does one wheel make between checks if he rides exactly 500 miles?

Question

A cyclist checks the air pressure of his 18-inch-diameter wheels every 500 miles during a cycling trip. How many rotations does one wheel make between checks if he rides exactly 500 miles? (Hint: there are 63,360 inches in a mile.

Answer 1

Hi, Sara,

 

Each time the wheel rotates once around, it has traveled the distance of its CIRCUMFERENCE - the length around the outside of the circle. So, what we really need to know for this question is the circumference of the wheel. Fortunately, the circumference and diameter of a circle are always related to each other. The ratio of a circle's circumference to its diameter is always equal to π (pi).

 

     Circumference  = pi

        diameter

 

Pi is an irrational number, usually abbreviated to 3.14. We can re-arrange this equation to solve for the circumference of this circle, since we know its diameter:

 

     Circumference = (pi) x (diameter)

 

     Circumference = (3.14) x (18 inches)

 

     Circumference = 56.5 inches (rounded)

 

Now, since we know how far the wheel travels for each rotation, we can use unit conversion to calculate how many rotations take place per 500 miles:

 

 

     500 miles x (63360 inches) x (1 rotation)

                             mile             56.5 inches

 

     500 miles x (63360 inches) x (1 rotation)
                             mile             56.5 inches

 

     = 560708 (rounded to the nearest digit) rotations every 500 miles

 

I hope this helps!

 

Andy

Answer 2

Hi Sara,

 

If the diameter of this wheel is 18", then the radius is 9".

 

This is important because wee need to determine the circumference of this tire.

 

C = 2πr

C = 2(3.14)(9) 

C = 56.52"

 

The cyclist checks his tires every 500 miles.  

Since there are 63,360 inches in a mile, 

500 mi (63360"/mi) = 31680000"

The cyclist check his tires every 31,680,000 inches

 

The circumference represents how far the tire goes in 1 rotation

Therefore 

31680000" /56.52 " per rotation = 560509.554 rotations

 

His tire mades 560,510 rotations in 500 miles.  This was rounded to a full rotation.