In a bucket and ball race, a bucket is placed at the starting point, which is 5 m from the first ball, and the other balls are placed 3 m apart in a straight line. There are ten balls in the line.

A competitor starts from the bucket, picks up the nearest ball, runs back with it, drops it in the bucket, runs back to pick up the next ball, runs to the bucket to drop it in, and she continues in the same way until all the balls are in the bucket. What is the total distance the competitor has to run?

[Hint : To pick up the first ball and the second ball, the total distance (in metres) run by a competitor is ]

Question

Philoid · Accepted Answer

The distance between the first ball and the bucket is 5m

So the competitor runs 10m (forward + backward)

The second ball the placed 3m ahead of first ball

For second ball he will 16.

Likewise, the distance covered by each ball is

3^rd = 22, 4^th = 28,….. 10^th = 64

Common difference (d) = 3^rd - 2^nd = 22-16 = 6

Here there are 10 balls to be picked so n = 10

Last term a₁₀ = 64

The sum of all the distance is given by S_n = (2a +(n-1)d)

=

= 5×(74) = 370

So the total distance covered by the competitor to pick all the is 370