Question

44. There are 25 trees at equal distances of 5 m in a line with a water tank,
the distance of the water tank from the nearest tree being 10 m. A
gardener waters all the trees separately, starting from the water tank
and returning back to the water tank after watering each tree to get
water for the next. Find the total distance covered by the gardener in
order to water all the trees.
10 m
5 m 5 m
25th tree​

Answer 1

ANSWER:-

Given:

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 waters all the trees separately starting from the well and here turns to the well after watering each tree to get water for the next.

To find:

Find the total distance the gardener will cover in order to water all the trees.

Solution:

⏺️Total number of trees=25

⏺️Distance between trees=5

⏺️Total distance between well & first tree is 10m.

Now,

gardener return back to well after watching each tree then,

⏺️Distance between well and second tree is, 10+ 10 +5 = 25

⏺️Distance between well and third tree=25+ 5+ 5= 35

⏺️Distance between well and fourth tree= 35 + 5 + 5= 45

Distance between well and last tree without return back;

=) 10 + 24(5) = 10+ 120= 130

So,

Common difference= 35 - 25= 10

Now,

Total distance covered by 24 trees,

We knew that,

${}^{S} n = \frac{n}{2} [2a + (n - 1)d]\\ \\ = > \frac{24}{2} [2(25) + (24 - 1)10] \\ \\ = > 12[50 + 23 \times 10] \\ \\ = > 12(50 + 230) \\ \\ = > 12(280) \\ \\ = > 3360$

Now,

Distance covered by 25 trees= 10+3360

=) 3370

Total distance covered by a gardener with return back= 3370+130

=) 3500m

Hence,

Total distance will covered by gardener is 3500m.

Hope it helps ☺️