Math Trail: |
Welcome to the Brock Pool Problem. This problem was created by students attending
the Math Camp at Brock University. |
This problem involves the pool at Brock University. To control how crowded the pool
is at anytime, the pool administrators have decided to take measurements of
the pool to determine how many people can comfortably fit in it. The shallow end
of the pool has a flat bottom, is 0.92m deep, and 15m in length. The width across
the pool is 18.3m. At the end of the shallow end there is a sudden drop off
to 1.22m in depth, and this section is 10.4m long. From the beginning of the
middle portion to the end of the deep end, it is 35m in length. The deep end has
a constant slope downwards, and the sloped portion is 2.48m long. The maximum
depth of the pool is 4m. We figured that the average person has a volume of about 0.093m³. The administrators want to know how many people could be crammed into the pool, if they are stacked on top of each other, filling the whole volume of the pool, and no one needs to breathe. They also want to know how many people can cover the surface of the water, if they are packed together arm next to arm and have their heads above the surface. Lastly, they want to know how many people can comfortably fit in the pool, so that all swimmers have enough room to tread water or swim. |
