Rita, John, and Adam share the cost of their new car. Rita pays half as much as John, who pays one-third as much as Adam does. What fraction of the total cost of the car does John pay?

Correct.
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The car costs
>$$\text{Total} = \text{Rita}+\text{John}+\text{Adam}=\$1+$2+$6 = $9$$.
John pays $2 out of that, so the final answer is $$\frac{2}{9}$$.

Incorrect.
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This answer choice is Rita's share of the cost.

Incorrect.
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Incorrect.
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All three are not paying equally, so this option is wrong.

Incorrect.
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$$\frac{1}{9}$$

$$\frac{2}{9}$$

$$\frac{2}{5}$$

$$\frac{1}{3}$$

$$\frac{3}{5}$$