There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener water 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.
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Answer:
The total distance the gardener will cover in order to water all the trees is 3500 m.
Step-by-step explanation:
Given :
Total numbers of trees = 25
Distance between each tree = 5 m
Distance between well and first tree = 10 m
The distance covered by the gardener to water the trees between the well and the first tree, second tree, third tree, fourth tree,...... are
2 × 10 , 2 ×(10 + 5) , 2 ×(10 + 5 + 5),......
i.e 20 , 30 ,40……..
[starting from the well and he returns to the well after watering each tree to get water for the next ]
Here, a = 20 , d = 30 - 20 = 10,
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S25 = 25/2 [2(20) + (25 – 1 10]
S25 = 25/2 [40 + 24×10]
S25 = 25/2 [40 + 240]
S25 = 25/2 × 280
S25 = 25 × 140
S25 = 3500 m
Hence, the total distance the gardener will cover in order to water all the trees is 3500 m.
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