There are 30 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 Gardner 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 Gardner will cover in order to water all the trees.
Hint:
Distances between trees and well are in A.P.
Given:
The distance of well from its nearest tree is 10 metres
Distance between each tree is 5 metres.
So,
In A.P
The first term is 10 metres and the common difference is 5 metres.
a = 10 & d = 5
The distances are in the following order
10, 15, 20… (30 terms)
The farthest tree is at a distance of $a+(30-1) \times d$
$I=10+(29) \times 5$
L = 155 metres.
Total distance travelled by the Gardner = 2×Sum of all the distances of 30 trees from the well.
Sum of distances of all the 30 trees is $\frac{\mathrm{n}}{2}\{\mathrm{a}+1\}$
Sum $=\frac{30}{2}\{10+155\}$ metres
$=15 \times 165$ metres
$=2475$ metres.
Total distance travelled by the Gardner is 2 × 2475 metres
∴The total distance travelled by the Gardner is 4950 metres