Problem 392

In step (i), Lavinia fills the $6
$\text{}$ L} bottle with water. In step (ii), she fills the 5 $\text{}$ L}$bottle from the$6 $\text{}$ L}$bottle, leaving the$6 $\text{}$ L}$bottle with$6 $\text{}$ L}-5 $\text{L =1}$ { L}$ of
water.

In step (iii), she empties the $5 $\text{}$
L}$bottle and so the$5 $\text{}$
L}$has no water and the$6 $\text{}$
L}$bottle still contains$1 $\text{}$
L}$.

In step (iv), she pours the $1 $\text{}$
L}$of water from the$6 $\text{}$
L}$bottle into the$5 $\text{}$
L}$ bottle.

After completing the sequence of four steps once, the $6 \text{ L}$ bottle contains no water and
the $5 \text{ L}$ bottle contains
$1 \text{ L}$ of water.

In the chart below, we continue to track the volume of water in each of
the two bottles following each step. Each volume of water is measured in
litres.

Step:
(i)
(ii)
(iii)
(iv)

$6 $\text{}$
L}$ bottle
$6$
$6-5=1$
$1$
$0$

$5 $\text{}$
L}$ bottle
$0$
$5$
$0$
$1$

Step:
(i)
(ii)
(iii)
(iv)

$6 $\text{}$
L}$ bottle
$6$
$6-4=2$
$2$
$0$

$5 $\text{}$
L}$ bottle
$1$
$5$
$0$
$2$

Step:
(i)
(ii)
(iii)
(iv)

$6 $\text{}$
L}$ bottle
$6$
$6-3=3$
$3$
$0$

$5 $\text{}$
L}$ bottle
$2$
$5$
$0$
$3$

After Lavinia completes the sequence of four steps a total of $3$ times, the volume of water in the $5 \text{ L}$ bottle is $3 \text{ L}$.