In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back to the pole and continues the same way until all the flags are on the pole. Find the total distance covered. [ 3 Marks]

Open in App

Solution

We have,
$d_{1}$ = distance travelled to pick up the first flag
= 10 + 10 = 2 $\times$ 10 = 20 m
$d_{2}$ = distance travelled to pick up the second flag
= 2 $\times$ (10 + 6) = 32m
$d_{3}$ = distance travelled to pick up the third flag
= 2 $\times$ (10 + 6 + 6)
= 44 m [ 1 Mark]
$d_{10}$ = distance travelled to pick up 10th flag
= 2 $\times$ [10 + (10 - 1) $\times$ 6]m = 128
This forms an A.P with a = 20, d = 12 and n = 10
$∴$ Total distance travelled
$= d_{1} + d_{2} + d_{3} + \dots + d_{10} [1 M a r k] S_{n} = \frac{n}{2} [2 a + (n - 1) d] = \frac{10}{2} [2 \times 20 + (10 - 1) 12] = 5 (40 + 108) = 5 \times 148$
= 740m [ 1 Mark]

Suggest Corrections

Similar questions

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are 10 Potatoes in the line. A competitor starts from the bucket, picks up the nearest potato runs back with it, drops it in the bucket, runs back to pick up the next potato runs to the bucket to drop it in, and the continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are $60^{\circ} a n d 30^{\circ}$ respectively. Find the height of the tower and the flag pole mounted on it.

In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back up the next flag and continues the same way until all the flags are on the pole. The total distance covered is

Q. In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag and comes back to the pole and runs for the next flag and continues the same way until all the flags are on the pole. The total distance covered is ____.

Join BYJU'S Learning Program