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Quiz of the Month (March 2003)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

     1.   3.2 mph
     2.   2.5 mph
     3.   4 mph

  Notes.
  1. Speed upstream   = 2 mph.  So time = 1/2 hr.
     Speed downstream = 8 mph.  So time = 1/8 hr.
     Total time = 1/2 + 1/8 = 5/8 hr.
     So average speed = 2/(5/8) = 3.2 mph

  2. Suppose current speed = v mph
     
     Speed upstream   = 5 - v mph.  Time = 1/(5 - v) hr.
     Speed downstream = 5 + v mph.  Time = 1/(5 + v) hr.
     But total time = 2/3.75 = 8/15 hr.
     So 1/(5 - v) + 1/(5 + v) = 8/15
     Solving, v = 2.5 mph

  
  3. On both legs of journey canoe must head
     into current at angle q as shown.
     Speed across river = AC = 4 mph by Pythag.
     So average speed = 4 mph

THIS MONTH'S QUIZ

1. A hiker walking along a railroad track comes to a tunnel. He gets 3/8 of the way into the tunnel when the sound of a train whistle behind him gives warning that the tunnel is not a safe place to be. A narrow width means death to anyone in it. He can run at 8 mph if need be, and has the choice of running back to the entrance or running to the other end. In either case the hiker will live, but just barely. How fast is the train travelling?

2. Two trains are travelling in opposite directions on parallel tracks. Train A is 210 m long and moving at 60 ms-1. Train B is 120 m long. The point on the track where the fronts of the trains pass each other is 30 m distant from the point where the rear of the trains pass each other. What can you say about the speed of train B?

3. The village of Southolme is 10 miles South of Middleholme, and Eastholme is 10 miles East of Middleholme. At 12 noon Andy sets off walking from Southolme to Middleholme at 2.25 mph, and at the same moment Betty sets off walking from Middleholme to Eastholme at 3 mph. At what time are Andy and Betty closest together?

***

(c) Hector C. Parr (2002)


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