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Example Questions
Example Question #41 : Other Mathematical Relationships
x varies inversely with y. When x=10, y=6. When x=3, what is y?
Inverse variation takes the form:
Plugging in:
Then solve when x=3:
Example Question #42 : Other Mathematical Relationships
The rate of speed is indirectly proportional to the time it takes to travel somewhere. If a person walks at a rate of 3 miles per hour and it takes them 4 hours to get to their destination how far did they travel?
For an indirect proportionality, use the equation
If rate of speed is indirectly proportional to the time, then the speed is y (3 miles per hour) and the time is x (4 hours).
Replace those into the indirect proportionality formula
Solve for k by multiplying by 4 on both sides
The person traveled 12 miles.
Example Question #43 : Basic Single Variable Algebra
A turtle moves at a pace that is inversely proportional to its weight. Suppose at five pounds it moves two feet per minute. What would be the turtle's speed in feet per minute if it weighed eight pounds?
Write the relationship for inverse proportionality. If one variable increases, the other variable must decrease.
or
Let be the turtle's speed, and is the weight of the turtle since the turtle's speed depends on its weight.
Solve for by substituting the initial conditions.
Multiply by two on both sides.
Substitute this value back into the original equation.
The relationship is:
Substitute eight pounds to find its speed.
The turtle will move at a rate of feet per minute.
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