PRIZE PUZZLE FOR OCTOBER 2007
THE BOAT TRIP
Dinner is being served at the Riverside Lodge but Johnny and his dad want to go sight-seeing down the river. Their motor boat has a maximum speed of 25 miles per hour and the river flows at 5 m.p.h. The cook calls out to them that they can go but must be back in half an hour. How far can they go down the river and still be back in time for dinner.?
ANSWERAs the river helps one way and hinders in the other by the same amount, one is tempted to say that the river flow makes no difference in which case we only have to work out how far the boat can travel in half an hour at 25 mph and halve the result. That leads to the answer 6.25 miles. But that is wrong.
No one fell for this trick and all solvers gave the right answer of 6 miles. If the answer is x miles then the time for this journey downstream is x/30 hours and the time to go back is x/20 hours. The sum of these two must be 0.5 hours. With a common denominator these two times are 2x/60 + 3x/60, a total of 5x/60 = x/12 hours which must equal 1/2 an hour so x = 12/2 = 6 miles.
Answers were received from Richard Burkhill, John Bownas, Clem Robertson and John Stafford (who won the draw). Many thanks to those members and thanks also for the answers to the Hot Key problem about the horseshoe which will be published in the next edition of Hot Key.