Perimeter and Area of Common Plane Figures

Perimeter and Area of Common Plane Figures

TGM Original Questions

A lawn mower has a blade of breadth \(0.75\) m, and its two front wheels are identical of diameter \(20\) cm, its two rear wheels are identical of diameter \(40\) cm. A gardener uses this lawn mower to mow a square lawn of dimension of \(18\) m by \(18\) m. He alternates his mowing directions, as shown in the figure below, at a speed of \(5\) m/min.

Assuming there is no overlapping of mowing areas, find

  1. the number of times he needs to move from one side to the opposite side of the lawn to finish mowing the whole area of the lawn,
  2. the number of rotations of the front and rear wheels, respectively, to finish mowing from one side to the opposite side, ignoring the length of the mower (giving your answers to the nearest integer),

  3. the least possible time needed for the gardener to fully mow the lawn.

Clarification for (c): the intended model counts time along the straight mowing strips only, excluding the turns and movement between strips. The source gives no turning model, so it does not determine the actual minimum total journey time.

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Answer:(a) 24 passes. (b) Front: 29 rotations; rear: 14 rotations (nearest integers). (c) 86.4 minutes excluding turns/transfers. Actual minimum time is not determined by the supplied model.

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