Question

The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 2-m beam can support 310 kg. How many kilograms can a 10-m beam support?

Answer 1

W = kL where W = weight supported, L = length of the beam and k is constant of variation.

Substituting the given values:-

310 = 2k
k = 155

so equation of variation is W = 155L

For length 10 m the weight it can support is

W = 155*10 = 1550 kg answer

Answer 2

62 kg.

Explanation:

Let w be the weight of beam and l be the length of beam.

We have been given that the weight that a horizontal beam can support varies inversely as the length of the beam.

We know that inversely proportion quantities are in form:
`y=(k)/(x)`, where k is constant of proportionality.

`w=(k)/(l)`

First of all, we will find the value of k using the
`w=310` and
`l=2` in inversely proportion equation as:

`310=(k)/(2)`

`310*2=(k)/(2)*2`

`620=k`

Now we will substitute
`620=k` and
`l=10`, in our given equation as:

`w=(620)/(10)`

`w=62`

Therefore, a 10-m beam can support 62 kilograms.