Question

Correct answers only please!

A person changed the size of the wheels on his motorcycle

He changed the size from a tire that had a 25 inch diameter to a tire that has a 28 inch diameter. He didn’t realize this would affect his speedometer and odometer. He didn’t re-calibrate either after changing the wheel size.

How fast is he really going on the new tires when his speedometer reads 60 mph?






A. 54 mph

B. 75 mph

C. 67 mph

D. 70 mph

Answer 1

C. 67 mph

Explanation:

∵ The ratio of speed of motorcycle and the circumference of the tyre is constant for a motorcycle,

If x be the speed ( in mph ) of a motorcycle having the tyre of diameter 28 inches,

⇒ The ratio of speed and circumference =
`(x)/(2\pi (14))`

( Because radius = Diameter / 2 ),

While, the speed of the same motorcycle having the tyre of diameter 25 inches is 60 mph,

⇒ The ratio of speed and circumference =
`(60)/(2\pi (12.5))`

By the above statement,

`(x)/(2\pi (14))=(60)/(2\pi (12.5))`

`\implies x=(60* 14)/(12.5)=(336)/(5)=67.2\approx 67`

So, the actual speed of the motorcycle after changing the tyre is 67 mph ( approx )

Hence, option 'C' is correct.

Answer 2

C. 67 mph

Explanation:

The speedometer reports speed based on the number of revolutions the tire makes in a given time period. If the motorcycle travels 28/25 times as far on each revolution, its speed is 28/25 times as great.

(28/25)(60 mph) = 67.2 mph ≈ 67 mph

_____

The distance traveled is proportional to the circumference of the tire, which is proportional to the diameter. Hence, actual speed for a given speedometer reading is proportional to the diameter of the tire.