Question

In a race, 20 balls are placed in a line at intervals of 4 meters, with the first ball 24 meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls?

Answer 1

Number of balls placed in a line = 20

Let A be the starting point.

The distance of the first ball from A = 24 m

The distance of the second ball from the first ball = 4 m
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A contestant starts from point A, travels a distance of 24 m and picks the first ball and brings it back to starting point A.

This is continued for each ball.

Distance travelled by the contestant to bring the first ball = 24 + 24 = 2 × 24 = 48 m

Distance travelled to bring the second ball = 2 (24 + 4) = 2 × 28 = 56 m

Distance travelled to bring the third ball = 2 × (24 + 4 + 4) = 64 m
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∴ The sequence of distances travelled are 48, 56, 64 ……………

This is an Arithmetic progression with first term a = 48,

Common difference d = 56 – 48 = 8,

Number of terms n = 20.

The sum of 20 terms of this A.P gives the total distance travelled by the contestant in bringing all balls to the starting place

S_n = `"n"/2[2"a" + ("n" - 1)"d"]`

S₂₀ = `20/2 [2 xx 48 + (20 - 1)8]`

= 10[96 + 19 × 8]

= 10[96 + 152]

= 10 × 248

= 2480

Total distance traveled = 2480 m