Math CentralQuandaries & Queries


Question from Marvel, a parent:

Tim is standing in a hole that is 4 feet deep. Ben asks him how much deeper is he going to dig the hole. Tim replies he will dig to the level that is 4 feet 2 inches deeper and that then the top of his head will be the same distance below ground level that it is now above. How tall is Tim?

Hi Marvel,

I took Tim's height to be $h$ feet and drew a sketch of him in the 4 foot hole. Hence the top of Tim's head is $h - 4$ feet above the ground.

Tim in the hole

Redraw the diagram with the hole 4 feet 2 inches deeper and the top of Tim's head $h - 4$ feet below the ground level. Use the diagram to write an equation for $h$ and then solve this equation.

Write back if you need more assistance,

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