A system of two 2000L holding tanks is set up with a pipe bringing water to the first tank, another pipe taking water from the first tank to the second, and a final pipe draining away from the second tank, with each pipe moving 100L/hr. Usually, the system holds nothing but pure water, with the tanks kept half-full. One day, an apprentice spilled a 10kg bag of salt at the mouth of the pipe feeding into the first tank. To add further injury to the original injury, the bag itself flew from his grasp and partially clogged the pipe draining from the second tank. If the pile of salt is being dissolved by the water at the rate of half of the remaining pile every three hours and if the drainage pipe now only carries 90L/h. ?(?) describes the mass of salt in the pile at the mouth of the first pipe. Set up an IVP for ?(?) and explain briefly. Then find the solution ?(?).
A system of two 2000L holding tanks is set up with a pipe bringing water to the first tank, another pipe taking water from the first tank to the second, and a final pipe draining away from the second tank, with each pipe moving 100L/hr. Usually, the system holds nothing but pure water, with the tanks kept half-full. One day, an apprentice spilled a 10kg bag of salt at the mouth of the pipe feeding into the first tank. To add further injury to the original injury, the bag itself flew from his grasp and partially clogged the pipe draining from the second tank. If the pile of salt is being dissolved by the water at the rate of half of the remaining pile every three hours and if the drainage pipe now only carries 90L/h. ?(?) describes the mass of salt in the pile at the mouth of the first pipe. Set up an IVP for ?(?) and explain briefly. Then find the solution ?(?).
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