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Chapter 7: Problem 48

Explain what is meant by joint variation. Give an example with your explanation.

Short Answer

Expert verified
Joint variation, or combined variation, is when a quantity varies directly as the product of two or more other quantities. For example, if the time taken to complete a task varies directly as the number of people and the amount of work, then doubling both the number of people and the amount of work would keep the time taken the same.

Step by step solution

01

Understanding Joint Variation

Joint variation, or combined variation, is when a quantity varies directly as the product of two (or more) other quantities. In other words, it can be represented in the form \( y = kxz \) where k is the constant of variation, and x and z are the variables.
02

Explaining the notion of Joint Variation

When we say 'y varies directly as x and z', it means that when x or z increase, y increases and when x or z decrease, y decreases. The aspect of 'direct' variation implies that the rate of increase or decrease is constant, and this constant rate is denoted by 'k' in equation \( y = kxz \). The constancy of 'k' ensures the direct proportional relationship among the variables.
03

Providing an example for Joint Variation

For instance, consider an example where the time taken to complete a task varies directly as the number of people and the amount of work. Let's say 10 people can complete a task in 5 hours. If we double both the number of people and the amount of work to 20 people and 10 hours respectively, the time taken remains the same(5 hours). This is because the quantity (time) varies directly as the product of the number of people and amount of work.

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