Robin's bike has wheels that are 25 inches in diameter. After the front wheel picks up a tack, Robin rolls another 154 feet and stops. How far above the ground is the tack?

Question

Robin's bike has wheels that are 25 inches in diameter. After the front wheel picks up a tack, Robin rolls another 154 feet and stops. How far above the ground is the tack?

Im having a hard time figuring out how to start? and picturing this problem

Answer 1

Hi Sophia,

Think about the problem like this- The tire is a circle with a circumference (length all the way around) of

C = π • D.

=3.14 • 25" = 78.5".

If the tack is on the ground when its picked up by the wheel, the wheel makes 23 complete revolutions, or turns, traveling a total distance of 1805.5" (I converted the 154 feet into 1,848 inches and then divided that by 78.5 to get 23). Each time the wheel turns, it travels 78.5".

The remainder is 1848-1805.5(23*78.5) = 42.5". That means that on its last turn before coming to a stop, the tack moved from the ground 42.5" up.

Picture a wheel moving across the screen to the right. The tack starts on the bottom. It moves all the way around 23 times, and then an additional 42.5". So the tack is 42.5" above the ground.

Answer 2

C = 25π in

154 ft = 1848 in

1848 in / 25π in = ?