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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 7.101 (page 1069)

Alice can paint a room in 6 hours. If Kristina helps her it takes them 4 hours to paint the room. How long would it take Kristina to paint the room by herself?

Short Answer

Expert verified

Kristina takes 12 hours to paint the room by herself.

Step by step solution

01

Given information

The problem has the information of the work done by Alice and Kristina.

02

Form the rational equation and solve

Use the given sentence to form the required rational equation.

As given, Alice(A) takes 6 hours to work alone whereas Alice(A) and Kristina(K) together take 4 hours.
Hence the equation is formed as $\frac{1}{6} + \frac{1}{K} = \frac{1}{4}$ .
Now solve equation (1) to find the time taken by Kristina(K) alone.

localid="1662473268596" $\begin{array}{rcl} \frac{1}{6} + \frac{1}{K} & = & \frac{1}{4} \\ \frac{1}{K} & = & \frac{1}{4} - \frac{1}{6} \\ = & \frac{6 - 4}{24} \\ = & \frac{2}{24} \\ = & \frac{1}{12} \\ K & = & 12 h o u r s \end{array}$

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Most popular questions from this chapter

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

$a . \sqrt{\frac{72}{98}} b . \sqrt[3]{\frac{24}{81}} c . \sqrt[4]{\frac{6}{96}}$

Simplify

(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Simplify the rational expression $\frac{8 m^{3} n}{12 m n^{2}}$ .

In the following exercises, simplify.

a. $\sqrt{48 b^{5}} - \sqrt{75 b^{5}}$

b. $8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$

In the following exercise, factor using substitution.

${(x - 3)}^{2} - 5 (x - 3) - 36$

See all solutions

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