Question

In a potato race, a bucket is placed at the starting point, which Is 5 m from the first potato. and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see fig, given below)

A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops ¡tin 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 potaotes are in the bucket. What is the total distance the competitor has to run? 

(Hint: To pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 +2 × (5 + 3)]

Answer 1

Total distance competitor taken to pick up the first potato = 5 + 5m 

= 2 × 5m. 

= 10m. 

Total distance taken by competitor to pick up the second potato 

= 5 + 3 + 3 + 5m. 

= 2 × 5 + 2 × 3 

= 2(5 + 3) = 2 × 8 

= 16m. 

∴ 10m. 16m, 22m 10^th potato 

a = 10, d = 16 – 10 = 6m. 

n = 10, S₁₀ = ?

= 5[20 + 9 × 6] 

= 5 [20 + 54] 

= 5 × 74 

∴ S₁₀ = 370 m. 

∴ Total distance the competitor has to run to pick up 10 potatoes is 370 m.