question archive In a period of heavy rainfall, water is pumped out of the downtown area and into the reservoir
In a period of heavy rainfall, water is pumped out of the downtown area and into the reservoir
Subject:MathPrice: Bought3
In a period of heavy rainfall, water is pumped out of the downtown area and into the reservoir. Suppose the pump, acting on its own, could fill the reservoir in 4 days. We now have multiple rates in, which we can account for by modifying the equation. Rate 1 In + Rate 2 In - Rate Out = Net Rate of Change We want to know if the reservoir is currently empty, after how many days of consecutive rainfall will the reservoir fill up? a. First, express the pump's contribution to the system as a rate. The time it takes for the pump to fill up the reservoir (by itself) is 4 days. At what rate, in reservoirs per day, does the pump work at? b. Once you have the rate, plug it into the equation below with the other two rates from the previous problem. Then solve for x. Rate 1 In + Rate 2 In - Rate Out = * 1 - The Engineer's Challenge Exercise 4. Suppose some time has passed and the reservoir is now no longer meeting the city's needs. The city is considering installing a canal which diverts water from the reservoir. The size of the canal (and its expense) is determined by the volume of water it needs to carry. This is where the city needs your help. They need to know how big to build the canal so that the reservoir doesn't fill up too quickly. The canal should be large enough so that, starting from empty, it would take two weeks of consecutive rainfall to fill the reservoir. The equation from the previous task is changed in a couple of ways. This time, you're left on your own to modify it. However, here are two hints. First, the canal is an additional "rate out". However, you don't know what rate the canal works at yet, since that is what you're trying to figure out. So this new rate out is unknown and hence a variable, so use Second, this time you know what the net rate of change is. You want the canal to fill up in 14 days. Express this as a rate. Modify the equation from Exercise 3 and compute the capacity of the canal so that the above condition is met. The capacity should be described in terms of number of days needed, working by itself, for it to drain the reservoir.
