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Mathsjam Jars
Age 14 to 16
Challenge Level 
Well done to Anurag and Christina for their
solutions to this problem:
The seven letters that take the same time to fill up are: I,L,O,E,M,T and H, all with a volume $14$cm$^3$ and thus taking $14$ minutes to fill.
The letter S takes the longest to fill up ($14.5$cm$^3$, $14.5$ minutes to fill).
The letter V fills up first ($13$cm$^3$, $13$ minutes to fill).
The letter A will take $13.5$ minutes to fill.
The graph corresponds to the letter M. Some points in the graph are over measured, for instance, the points between 4 and 5 cm.
The seven letters that take the same time to fill up are: I,L,O,E,M,T and H, all with a volume $14$cm$^3$ and thus taking $14$ minutes to fill.
The letter S takes the longest to fill up ($14.5$cm$^3$, $14.5$ minutes to fill).
The letter V fills up first ($13$cm$^3$, $13$ minutes to fill).
The letter A will take $13.5$ minutes to fill.
The graph corresponds to the letter M. Some points in the graph are over measured, for instance, the points between 4 and 5 cm.
1. 0 - 3 minutes - filling one
'leg' of M, with rate of height increase constant due to constant
width
2. 3 - 7 minutes - further water
will run over in to the central dip of the M, and then once this is
filled into the opposite leg. These have a combined volume of
$4$cm$^3$ and so take 4 minutes to fill
3. 7 - 11 minutes - water fills top
rectangular section with constant rate of height increase
4. 11 - 14 minutes - filling up top
two trapezoidal sections of M
5. 14 - 16 minutes - letter
completely full - no further height gain
Section 4 in the period 11-14 minutes should actually be
represented by a curved line on the chart as the width of the
section being filled is changing with height, and therefore so will
the rate of height increase.
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