X can complete a project in 14 days, Y in 10 days. When Z joins them, the work is finished in 3.5 days. How many days would Z need alone?

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1. Write each worker's rate: $X=1/14$, $Y=1/10$.

2. Sum X and Y: $1/14+1/10=6/35$ (work per day).

3. All three finish in $3.5$ days, so their combined rate is $1/3.5=2/7=10/35$.

4. Z's rate = $10/35-6/35=4/35$. So Z alone needs $35/4=8.75$ days.

FINAL_ANSWER: b

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