The total length of the shortest piece and longest piece is...?

Question

A length of rope 8.4 meters long is cut into three pieces whose lengths are in proportion 2:6:8. The total in length of the shortest piece and longest piece is what?

Answer 1

Write a variable for each piece of the rope: 

 

L₁ L₂ and L_3. 

 

The lengths have to add up to 8.4 meters: 

 

L1 +L2 + L3 = 8.4 

 

We have three unknown quantities, so we will need 3 equations. Therefore, use the ratios given to write down two more equations containing the variables: 

 

L1/L2 = 2/6          L1=L2(1/3)

 

L2/L3 = 6/8         L2 = L3(3/4)

 

Now solve the system: 

 

L1 +L2 + L3 = 8.4

L1 = L2(1/3)

L2 = L3(3/4)