# Plep's Puzzles

Name:

## Tuesday, March 08, 2005

### Fox and Hen

A hen and a fox have a combined age of 91.

The fox is now twice the age of the hen when the fox was as old as the hen is now.

How old are they?

(This puzzle found on the back of a beermat).

iok said...

hen:39
fox:52

thx for the puzzle, plep.

March 10, 2005 at 5:18 AM
Anonymous said...

Yep.

f + h = 91.
therefore f = 91 - h

f = 2(h - (f - h) )

91 - h = 2(h - (91 - h - h) )

etc.

- plep

March 15, 2005 at 9:18 AM
Anonymous said...

Assume:
age of hen now = a
age difference = b
age of fox now = a + b
age of hen then = c

Age of hen now add age of fox now is 91:
(a) + (a + b) = 91
a + a + b = 91
2a + b = 91 -- (1)

Fox is now twice as hold as the hen was:
a + b = 2c -- (2)

"Fox was as old as the hen is now:" Hen is a, so fox was a too; hen was c; age difference is b:
a = c + b
c = a - b -- (3)

substitute (3) into (2):
a + b = 2(a - b)
a + b = 2a - 2b
b = a - 2b
3b = a
a = 3b -- (4)

substitute (4) into (1):
2(3b) + b = 91
6b + b = 91
b = 91/7
b = 13
======

substitute b into (1):
2a + 13 = 91
a = (91 - 13)/2
a = 39
======

Age of hen is a = 39
Age of fox is a + b = 39 + 13 = 52

December 8, 2005 at 2:58 AM