Mathematical & Logical Puzzles -Q2

5.   The Professor On The Escalator

            When Professor Stanislaw Slapernarski, the Polish mathematician walked very slowly down the down-moving escalator, he reached the bottom after taking 50 steps.  As an experiment, he then ran up the same escalator one step at a time, reaching the top after taking 125 steps. 

            Assuming that the Professor went up five times as fast as he went down (i.e. he took five steps to every one before), and that he made each trip at a separate constant speed, how many steps would be visible if the escalator stopped running?

6.   The Encounter On The Bridge

            On a foggy night, a passenger car and a truck meet on a bridge which is so narrow that the two vehicles can neither pass nor turn.  The car has proceeded twice as far onto the bridge as the truck, but the truck has required twice as much time as the car to reach this point.  Each vehicle has only half its forward speed when in reverse.  Which of the two vehicles should back up to allow both of them to cross the bridge in the minimum time?

7.   The Early Commuter

            A commuter is in the habit of arriving at his suburban station each evening at exactly five o’clock.  His wife always meets the train and drives him home.  One day he takes an earlier train and arrives at his station at four o’clock.  The weather is pleasant so instead of telephoning home, he starts walking along the route always taken by his wife.  They meet somewhere along the way. 

            He gets into the car and they drive home arriving ten minutes earlier than they usually do.  Assuming that the wife always drives with a constant speed, and on this particular occasion she left just in time to meet the five o’clock train, can you determine how long the husband walked before he was picked up?

8.   The Two Ferryboats

            Two ferryboats start at the same instant from opposite sides of the river travelling across the water en route at right angles to the shores.  Each travels at a constant speed but one is faster than the other.  They pass at a point 720 metres from the nearest shore.  Both boats remain at their slips for ten minutes before starting back.  On the return trip, they pass 400 metres from the other shore.  How wide is the river?

Check Out The Answers