Wheel circumference

The circumference of the first wheel is 0.5 m larger than the circumference of the second wheel. The first wheel turns on the 36 m track as many times as the second on the 30 m track. Determine the rims of both wheels.

Final Answer:

a =  3 m
b =  2.5 m

Step-by-step explanation:

$$\begin{gathered} 36/a=30/b \\ a=0.5+b \\ 36\cdot b=30\cdot a \\ a=0.5+b \\ 30a-36b=0 \\ a-b=0.5 \\ Row2-\frac{1}{30}\cdot Row1\to Row2 \\ 0.2b=0.5 \\ b=\frac{0.5}{0.2}=2.5 \\ a=\frac{0+36b}{30}=\frac{0+36\cdot 2.5}{30}=3 \\ a=3 \\ b=\frac{5}{2}=2.5 \end{gathered}$$

$b=2.5=2.5\text{m}$

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