91Ó°ÊÓ

For Problems \(33-50\), set up an equation and solve the problem. (Objective 2 ) Rita jogs for 8 miles and then walks an additional 12 miles. She jogs at a rate twice her walking rate, and she covers the entire distance of 20 miles in 4 hours. Find the rate she jogs and the rate she walks.

For Problems 1-40, perform the indicated operations and express answers in simplest form. $$ \frac{3}{x-5}-\frac{4}{x+7}+\frac{3 x-27}{x^{2}+2 x-35} $$

Add or subtract as indicated and express your answers in simplest form. (Objective 3) $$\frac{3 y}{4}+\frac{7 y}{5}$$

Perform the indicated multiplications and divisions and express your answers in simplest form. $$\frac{2 x^{2}-6 x-36}{x^{2}+2 x-48} \cdot \frac{x^{2}+5 x-24}{2 x^{2}-18}$$

\(\frac{h}{4}+\frac{h}{5}-\frac{h}{6}=1\)

Simplify each algebraic fraction. $$\frac{8 x^{2}-51 x+18}{8 x^{2}+29 x-12}$$

Simplify each algebraic fraction. $$\frac{10 a^{2}+a-3}{15 a^{2}+4 a-3}$$

The numerator of a fraction is 8 less than the denominator. The fraction in its simplest form is \(\frac{5}{6}\). Find the fraction.

For Problems \(33-50\), set up an equation and solve the problem. (Objective 2 ) A water tank can be filled by an inlet pipe in 5 minutes. A drain pipe will empty the tank in 6 minutes. If by mistake the drain is left open as the tank is being filled, how long will it take before the tank overflows?

For Problems 41-60, simplify each of the complex fractions. $$ \frac{\frac{1}{2}-\frac{3}{4}}{\frac{1}{6}+\frac{1}{3}} $$