You may also like

problem icon

On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

problem icon

Parabolic Patterns

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

problem icon

More Parabolic Patterns

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

Mathsjam Jars

Stage: 4 Challenge Level: Challenge Level:1
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.

Letter M

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.