May 2014
Problem of the Month

Jack and Jill

Jack and Jill raced up and down a hill that was 440 yards from top to bottom.

Jill got to the top first, immediately started down, and met Jack 20 yards from the top.

She beat Jack to the bottom of the hill by half a minute.

Both runners were able to run down hill one-half again faster than they ran up.


How long did it take Jill to run the full half mile of 880 yards?

Solution to the Problem:

The answer is: Jill would take 6.3 minutes or 6 minutes 18 seconds to run the 1/2 mile.

Let x = Jill's rate going up the hill.   Then her rate down the hill would be 1.5x.
Let y = Jack's rate going up the hill.   Then his rate down the hill would be 1.5y.

Equate Jill's time when she meets Jack with Jack's time when he meets Jill.
Then equate Jill's total time plus 1/2 minute with Jack's total time.

Correctly solved by:

1. James Alarie

Flint, Michigan

Send any comments or questions to: David Pleacher