Question

in a potato race, a bucket is placed at the starting point, which is 5 m from the
and the other potatoes are placed 3 m apart in a straight line. There are ten po
line (see Fig. 56)
eren potatoes
Fig. 5.6
​

Answer 1

Answer:

The Total distance the competitor has to run to pickup all the potatoes is 370 meter.

Step-by-step explanation:

Distance run to pickup the first potato = 5 * 2 = 10 m (Both Sides)

Distance run to pickup the second potato = 5 + 3 = 8

= 8 * 2 = 16 m (Both Sides

Distance run to pickup third potato = 8 + 3

= 11 * 2 = 22 m (Both Sides)

Therefore, the distances covered are in an AP as follows:

10,16,22.......

So we can calculate the distance ran by her to pickup 10 Potatoes.

We can use the formula:

Sn = n/2(2a + (n - 1)d)

Here,

a = 10           d = 6             and         n = 10

Sn = 10/2((2)(10) + (10 - 1)(6))

Sn = (5)(20 + (9) (6))

Sn = (5)(20 + 54)

Sn = (5)(74)

Sn = 370

Therefore, the Total distance the competitor has to run to pickup all the potatoes is 370 meter.

Answer 2

$\Large{\underline{\underline{\bf{Given:-}}}}$

In a potato race, a bucket is placed at the starting point, which is 5 m from the and the other potatoes are placed 3 m apart in a straight line.

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$\Large{\underline{\underline{\bf{To\: Find:-}}}}$

Total distance covered by the competitor = ?

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$\Large{\underline{\underline{\bf{Solution:-}}}}$

⋆The distance of first potato from the starting point = 5 meters

⋆Therefore, the distance covered by competitor to pick up first potato and put it in bucket = 5 × 2 = 10 meters

⋆The distance of third potato from the starting point = 8 + 3 = 11 meters

⋆Therefore, the distance covered by competitor to pick up 3rd potato and put it in bucket = 11 × 2 = 22 meters.

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$\Large{\underline{\underline{\bf{Therefore, \: we \: have \: sequence:-}}}}$

$10 + 16 + 22 + ...10 terms$

(There are ten terms because there are ten potatoes)

$\Large{\underline{\underline{\bf{To \:calculate\: the\: total\: distance\: covered :-}}}}$

$⟹a = 10 \\ \\ ⟹d = 16 - 10 = 6 \\ \\ ⟹n = 10$

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$\Large{\underline{\underline{\bf{By \: using\: formula:-}}}}$

$⟹s_n = \frac{n}{2} [2a + (n - 1)d ]\\ \\⟹ s_{10} = \frac{10}{2} [2(10) + (10 - 1)6] \\ \\⟹ s_{10} = \frac{10}{2}[ 20 + (9)6 ]\\ \\ ⟹s_{10} = 5(20 + 54) \\ \\ ⟹s_{10} = 5 \times 74 \\ \\ ⟹s_{10} = 370$

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$\boxed{\Large{\red{s_{10}=370}}}$

➦Therefore, total distance covered by competitor is equal to 370 meters

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$\Large{\underline{\underline{\bf{Thanks}}}}$