Oil Line Puzzle Instructions

Congruent triangles can be used to find the shortest distance. Consider the case of an oil company that needs to pump oil from the main line to two different stations, A and B. A single pumping station can tap into the line and pump oil to these locations (A and B). Where is the best place to put the station so you lay the least amount of pipe?
  1. Load OilLine.html in Netscape (NOT version 4 of MS Internet Explorer..there are Java bugs in this version)

  2. Locate location A at (125,25) and location B at (235,50)

  3. Put the Station half way between 125 and 235. What location is the Pumping Station? What is the length of pipe needed? Do you think this is the least possible?

  4. Click "Show Hint" (if you can't see the hint, press the "Hide Map" button too). Move the Pumping Station so that it is in line with the hint. Where is the Pumping Station location now? What is the length of pipe needed now?

  5. Move the Station a little to the left and then to the right, noting what happens to the length of pipe needed. Where is the best place to put the station? Why?

  6. Change Location B to (35,35). Without the hint showing, try to find the best place to put the Pumping Station. Where should it be placed?

  7. Now move A to (25,10) and B to (200,50). Where should the Pumping Station be placed now?

  8. Check your answer with the hint. Do you see any relation between the angles in this situation and the billiards?

  9. If the angle between the pumping station and location A is 35 degrees, what is the angle from location A to location B?

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