Question

When placed end to end, three red rods are 2 cm longer than than 2 blue rods. Three blue rods are 2 cm longer than four red rods. How long is each rod?

Answer 1

Red = 10 cm, blue = 14 cm

Explanation:

Let the length of each red rod be r and each blue rod be b

Then we have:

• 3r - 2b = 2
• 3b - 4r = 2

Multiply the first equation by 3 and the second one by 2:

• 9r - 6b = 6
• 6b - 8r = 4

Add the equations to eliminate one of variables:

• 9r - 8r = 6 + 4
• r = 10 cm

Find the value of b:

• 3*10 -2b = 2
• 30 - 2 = 2b
• 2b = 28
• b = 14 cm