Question

There are 25 trees at equal distance 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.

 

Answer 1

Distance covered by the gardener to water the first tree and return to the water tank
=10m+10m = 20m
Distance covered by the gardener to water the second tree and return to the water tank
=15m+15m =30m
Distance covered by the gardener to water the third tree and return to the water tank
= 20m+ 20m= 40mand so on.
∴Total distance covered by the gardener to water all the trees =20m+30m+40m+...... up
to 25 terms
This series is an arithmetic series.
Here, a = 20,d = 30-20 =10 and n = 25

`"Using the formula"    S_n= n/2 [2a +(n-1)d,] ` we get

`S_25 = 25/2[2xx20+(25-1)xx10]`

`=25/2(40+240)`

=`25/2=280`

=3500

Hence, the total distance covered by the gardener to water all the trees 3500 m.