Question

Ally's tricycle has two different wheel sizes: one larger wheel and two smaller wheels. As Ally travels the distance between her house and her neighbor's house on the tricycle, the larger wheel revolves 10 times and each of the smaller wheels revolve 25 times. If half the circumference of the larger wheel is 5 inches more than the circumference of one of the smaller wheels, what is the distance, in inches, traveled by the tricycle between Ally's house and her neighbor's house?

Answer 1

Answer:

500 inches

Step-by-step explanation:

Let C₁ and n₁ be the circumference and the number of rotations of the larger wheel. Also, let C₂ and n₂ be the circumference and the number of rotations of the smaller wheel. Since the distance moved by both wheels from Ally's house to her neighbor's house is the same, n₁C₁ = n₂C₂. (1)

Also it is given that half the circumference of the larger wheel is 5 inches more than the circumference of one of the smaller wheels.

So, C₁/2 = C₂ + 5

C₁ = 2(C₂ + 5)  (2)

Substituting C₁ into (1), we have

n₁C₁ = n₂C₂.

n₁[2(C₂ + 5)] = n₂C₂.

Since n₁ = 10 and n₂ = 25, we have

10[2(C₂ + 5)] = 25C₂

20(C₂ + 5) = 25C₂

expanding the bracket,

20C₂ + 100 = 25C₂

collecting like terms, we have

25C₂ - 20C₂ = 100

5C₂ = 100

dividing both sides by 5, we have

C₂ = 100/5

= 20 inches

So, the distance between Ally's house and her neighbor's house is d = n₂C₂ = 25(20)

= 500 inches