IM Alg2.2.21 Lesson: Rational Equations (Part 2)

Noah likes to go for boat rides along a river with his family. In still water, the boat travels about 8 kilometers per hour. In the river, it takes them the same amount of time  to go upstream 5 kilometers as it does to travel downstream 10 kilometers. If the speed of the river is , write an expression for the time it takes to travel 5 kilometers upstream and an expression for the time it takes to travel 10 kilometers downstream.

Use your expressions to calculate the speed of the river. Explain or show your reasoning.

Circuits in parallel follow this law: The inverse of the total resistance is the sum of the inverses of each individual resistance. We can write this as:   where there are  parallel circuits and  is the total resistance. Resistance is measured in ohms. Two circuits are placed in parallel. The first circuit has a resistance of 40 ohms and the second circuit has a resistance of 60 ohms. What is the total resistance of the two circuits?

Two circuits are placed in parallel. The second circuit has a resistance of 150 ohms more than the first. Write an equation for this situation showing the relationships between  and the resistance  of the first circuit.

For this circuit, Clare wants to use graphs to estimate the resistance of the first circuit  if  is 85 ohms. Describe how she could use a graph to determine the value of  and then follow your instructions to find .

Two circuits with resistances of 40 ohms and 60 ohms have a combined resistance of 24 ohms when connected in parallel. If we had used two circuits that each had a resistance of 48 ohms, they would have had that same combined resistance. 48 is called the harmonic mean of 40 and 60. A more familiar way to find the mean of two numbers is to add them up and divide by 2. This is the arithmetic mean. Here is how each kind of mean is calculated: