Question

In a potato race, a bucket is placed at the starting point, which is 5 meters from the first potato, and the other potatoes are placed 3 meters apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

• A. 370 m
• B. 400 m
• C. 350 m
• D. 320 m

Answer 1

The correct option is A

370 m

The distance of first potato from the starting point = 5 meters
All potatoes are 3 meters apart from each other.
Distance of second potato from the starting point = 5 + 3 = 8 metres
Distance of third potato from the starting point = 8 + 3 = 11 metres

Therefore, the sequence is 5, 8, 11, ... 10 terms (There are ten terms because there are ten potatoes)

The sum of this progression is given by
$S_n=\frac{n}{2}(2a_0+(n-1\left)d\right)$
$\Rightarrow \frac{10}{2}\left(2\right(5)+(10-1\left)\right(3\left)\right)$
$\Rightarrow 5(10+9(3\left)\right)$
$\Rightarrow 5\left(37\right)\Rightarrow 185$

Since the competitor has to run back each time a potato is collected to drop it in the bucket, the competitor effectively runs two times the total distance.
Therefore the total distance ran is, $=185\times 2=370m$