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In a potato race, a bucket is placed at the starting point, which is $5\text{ m}$ from the first potato, and the other potatoes are placed $3\text{ m}$ apart in a straight line. There are ten potatoes in the line as shown. What total distance does the competitor run to bring all potatoes back to the bucket? 
A$320\text{ m}$
B$350\text{ m}$
C$370\text{ m}$
D$390\text{ m}$
Answer & Solution
Correct answer: C. $370\text{ m}$
The potato distances from the bucket are $5,8,11,\ldots$ for 10 potatoes, so they form an AP with $a=5$, $d=3$, $n=10$. Since the competitor runs to each potato and back, total distance is twice the sum of these distances.
1. Sum of distances to the potatoes:
$$S_{10}=\frac{10}{2}[2\cdot 5+(10-1)\cdot 3]=5(10+27)=185.$$
2. Total running distance:
$$2\times 185=370\text{ m}.$$
Option B is tempting if one incorrectly counts only one-way distances for some trips. Option D can arise from using 11 potatoes by mistake. Option A comes from a wrong AP sum. So the correct total is $370\text{ m}$.
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