Question

At an ultraviolet, or UV, rating of $4,$ those people who are moderately sensitive to the sun will burn in 70 min. Given that the number of minutes it takes to burn, $t$, varies inversely with the UV rating, $u,$ how long will it take moderately sensitive people to burn when the UV rating is $14 ?$

Name: Problem 65, Chapter 7: Elementary and Intermediate Algebra
Uploaded: 2020-07-22T03:31:32-08:00
Duration: 2 min 7 s
Channel: Cassandra Whitehead
Description: At an ultraviolet, or UV, rating of 4, those people who are moderately sensitive to the sun will burn in 70 min. Given that the number of minutes it takes to burn, t, varies inversely with the UV rating, u, how long will it take moderately sensitive people to burn when the UV rating is 14 ?

   At an ultraviolet, or UV, rating of $4,$ those people who are moderately sensitive to the sun will burn in 70 min. Given that the number of minutes it takes to burn, $t$, varies inversely with the UV rating, $u,$ how long will it take moderately sensitive people to burn when the UV rating is $14 ?$

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 7, Problem 65

Instant Answer

Solved by Expert Cassandra Whitehead

07/22/2020

Step 1

This can be represented by the equation $t = \frac{k}{u}$, where $k$ is the constant of variation. Show more…

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At an ultraviolet, or UV, rating of $4,$ those people who are moderately sensitive to the sun will burn in 70 min. Given that the number of minutes it takes to burn, $t$, varies inversely with the UV rating, $u,$ how long will it take moderately sensitive people to burn when the UV rating is $14 ?$

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Key Concepts

Constant of Proportionality

The constant of proportionality is a fixed number that relates two variables in an inverse variation equation. It is determined using known values from the relationship, and once calculated, it can be used to find unknown values of one variable when the other is given.

Setting Up and Solving Equations

This concept involves substituting known values into the inverse variation formula and manipulating the equation to solve for the unknown variable. Mastery of basic algebraic techniques is essential for setting up the equation correctly and isolating the desired variable.

Inverse Variation

Inverse variation describes a relationship between two variables where their product is constant, meaning that as one variable increases, the other decreases proportionally. It is commonly expressed by the equation t = k/u, where t is one variable, u is the other, and k is the constant of proportionality.

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