PRIZE PUZZLE FOR MAY 2007

JANE AND BOB

Jane and Bob set off on a car journey at the same time and arrive at their destination at the same time, covering the same distance. Being a long journey they each decide to take a break but for different periods of time. For the whole journey, Jane was driving twice as long as Bob was taking a break whilst Bob was driving for three times the time that Jane was taking a break. Who drove the faster?

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ANSWER 

Let J be the proportion of the journey time that Jane was taking
a break.  Let B be the proportion of the journey time that Bob
was taking a break.

1-J is therefore the proportion of the journey time Jane was
driving.  Jane was driving twice as long as Bob was taking a
break, so  1-J = 2B

Similarly, 1-B = 3J

Solving these two equations makes J = 1/5 and B = 2/5

So Jane was driving for 4/5ths of the journey time and Bob was
driving for 3/5ths.  As Bob was driving for the shorter time
period for the same distance, he was driving the faster on
average.  So the answer is Bob.

I received a good number of answers this time, maybe because I republished the puzzle on the Yahoo mailing list a week before the closing date.

Correct answers were received from Clem Robertson, Rob Webb, Peter Greenhalph, Brett Clark and Barry Cant, who won the draw.

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