Henry Ernest Dudeney/Puzzles and Curious Problems/354 - The Wheels of the Car/Solution

by : $354$

 * The Wheels of the Car

Solution
The fore-wheel was $15$ feet in circumference, while the hind-wheel was $18$ feet in circumference.

Proof
We have that $120$ yards is $360$ feet.

We need to find $a$ and $b$ which are divisors of $360$ such that $a n = b \paren {n + 4}$.

We have that:

Thus we see that:
 * $15 \times \paren {20 + 4} = 18 \times 20$

Reducing $15$ and $18$ by $3$ each gives $12$ and $15$, where:


 * $12 \times \paren {24 + 6} = 15 \times 24$

confirming and corroborating our inkling that the circumferences were $15$ and $18$ feet respectively.