Rope p is 3 times as long as rope q. Rope q is 1m 10 cm shorter than rope r. Rope r is 1 m 30 cm shorter than rope p. What is the length of rope q? Express your answer in meters and centimeters
p=3q
q = r-1.1
r = p-1.3
q = p-1.3-1.1
q = 3q-2.4
...
Is 56cm
p=3q
q = r-110
r = p-130
q = p-130-110
q = 3q-240
240+q = 3q
240 = 2q
120 = q
To find the length of rope q, we need to understand the relationship between ropes p, q, and r.
Let's assign variables to the lengths of the ropes:
Length of rope p = x
Length of rope q = y
Length of rope r = z
According to the given information:
1. Rope p is 3 times as long as rope q: x = 3y
2. Rope q is 1m 10cm shorter than rope r: y = z - 1m 10cm
3. Rope r is 1m 30cm shorter than rope p: z = x - 1m 30cm
We want to find the length of rope q (y).
Let's substitute the values from equations (1) and (3) into equation (2) to derive an expression containing only y:
3y = z - 1m 10cm
Since z = x - 1m 30cm, we can substitute that as well:
3y = (x - 1m 30cm) - 1m 10cm
3y = x - 1m 30cm - 1m 10cm
3y = x - 2m 40cm
Now, let's substitute the value of x from equation (1) into the derived equation:
3y = 3y - 2m 40cm
Since we get 3y on both sides of the equation, we are left with 0 = -2m 40cm.
This equation implies that the length of rope q (y) is 0 meters and -2 meters and 40 centimeters, which is not possible.
Hence, there seems to be an inconsistency with the given information or an error in the problem statement. Please verify the information provided or provide additional details to resolve the issue.