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Rates of Change, SMB-009

The number of trees that can be planted along the fence line of a paddock varies inversely with the distance between each tree.

There will be 108 trees if the distance between them is 5 metres.

  1. How many trees can be planted if the distance between them is 6 metres?  (2 marks)

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  2. What is the distance between the trees if 120 trees are planted?  (1 mark)

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Show Answers Only
  1. `90`
  2. `4.5\ text(metres)`
Show Worked Solution

i.   `t prop 1/d`

`t` `= k/d`
`108` `= k/5`
`k` `= 540`

 
`text(Find)\ t\ text(when)\ d = 6:`

`t` `= 540/6`
  `= 90`

 

ii.   `text(Find)\ d\ text(when)\ t = 120:`

`120` `= 540/d`
`d` `= 540/120`
  `= 4.5\ text(metres)`

Filed Under: Variation and Rates of Change Tagged With: num-title-ct-patha, smc-4239-30-a prop 1/b

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