Question

In a potato race a bucket is placed at the starting point. It is $5m$ away from the first potato. The rest of the potatoes are placed in a straight line each $3m$ away from the other. Each competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick the next potato, runs to the bucket to drop it in, and she continues in the same way till all the potatoes are in the bucket. What is the total distance covered if $15$ potatoes are placed in the race?
If the distance covered is $1340m$, find the number of potatoes?

Answer 1

First potato is at distance of "5m"

second potato is at distance of"8m"

i.e, a = 5m; d = 3m

Also given competitor starts from bucket

runs back, to pick the next next potato

runs to the bucket to drop it in

i.e, Total distance travelled

$S=\frac{2n}{2}[2a+(n-1\left)d\right]$

$S=n[2a+(n-1\left)d\right]$

distance traveled if 15 potatoes are placed

$S=15[2\times 5+14\times 3]$

$S=780m$

If S = 1340; n =?

$1340=n[2\times 5+(n-1\left)3\right]$

$1340=10n+3n^2-3n$

$3n^2+7n-1340=0$

$n=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-7\pm \sqrt{49+4\times 134\times 3}}{2\times 3}$

$=20$ or $\frac{-67}{3}$

$\Rightarrow n=20$