The front wheel of a tricycle has a circumference of 63 inches, and the back wheels have a circumference of36 inches. If points P and Q are both touching the sidewalk when Felicity starts to ride, how far will she have ridden when P and Q first touch the sidewalk at the same time again?

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The front wheel of a tricycle has a circumference of 63 ​inches, and the back wheels have a circumference of36 inches. If points P and Q are both touching the sidewalk when Felicity starts to​ ride, how far will she have ridden when P and Q first touch the sidewalk at the same time​ again?

SabadisO · Accepted Answer

The circumference of the front wheel is 2⋅63⋅π=126π inches and of the back wheel is 2⋅36⋅π=72π inches. Therefore if the front wheel does m full turns, for m a natural number, the tricycle moves m⋅126π inches, and if the back wheel does n full turns the tricycle moved π⋅72π. The points P and Q then touch the sidewalk at the same time for m and n such that m⋅126π=n⋅72π, which is equivalent, by dividing both sides by 18π, to m⋅7=π⋅4, Since the minimal common multiple of 7 and 4 is 25 we have that the smallest m and n satisfying this equations are m=4 and n=7. Therefore Felicity will have ridden 4⋅126π=504π inches when P and Q frst touch the sidewalk at the same time.

The front wheel of a tricycle has a circumference of 63 inches, and the back wheels have a circumference of36 inches. If points P and Q are both touch

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