There are 25 trees at equal distances of 5 meters in a line with a well,the distance of the well from the nearest tree being 10 meters. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

Assume that Gardner is standing near the well initially and he did not return to the well after watering the last tree.

Distance covered by Gardner to water 1^st tree and return to the initial position = 10 m + 10 m = 20 m

Distance covered by Gardner to water 2^nd tree and return to the initial position = 15 m + 15 m = 30 m

Distance covered by Gardner to water 3^rd tree and return to the initial position = 20 m + 20 m = 40 m

∴Distances covered by the Gardner to water the plants are in A.P.

Here a = 20, d = 10

Distance covered to water 25^th tree = 20 + (25 – 1) x 10 = 20 + 240 =260

Total distance covered by the Gardner

= 25/2 [2 x 20 + (25 - 1) x 10] - 260

= 2740

 

Thus, the total distance covered by the Gardner is 2740 m.