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When 2 pieces of rope are placed end to end the measure 40 meters in length. When the 2 pieces are laid side by side, one is 10 meters longer than the other. How long is each piece of rope?

Respuesta :

Answer:

Length of Rope 1 = 15 meters

Length of Rope 2 = 25 meters

Step-by-step explanation:

Lets say length of rope 1 = L₁

and the length of rope 2 = L₂

Using the given information,

L₁ + L₂ = 40 ....................................(Eq. 1)

L₂ = L₁ + 10 .....................................(Eq. 2)

substituting Eq. 2 in Eq. 1,

L₁ +  L₁ + 10 = 40

2L₁ + 10 = 40

2L₁ = 30

Thus, L₁ = 15

Length of Rope 1 = 15 meters

Length of Rope 2 = 25 meters

fichoh

Using a system of equations, the length of each rope would be 15 and 25 meters respectively.

Let the Parameters be ; a and b

  • a + b = 40 - - - - (1)
  • a = b + 10 - - - - (2)

From (2) ___

Substitute a = b + 10 into equation (1)

a + b = 40

(b + 10) + b = 40

b + 10 + b = 40

2b + 10 = 40

2b = 40 - 10

2b = 30

b = (30 ÷ 2)

b = 15

From (2)

a = b + 10

a = 15 + 10

a = 25

Therefore, the length of each rope will be 15 and 25 meters.

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