Chapter 7

Each exercise is a problem involving motion. How bad is the heavy traffic? You can walk 10 miles in the same time that it takes to travel 15 miles by car. If the car's rate is 3 miles per hour faster than your walking rate, find the average rate of each. (TABLE CANNOT COPY)

Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(g\) varies directly as \(h\)

Find the least common denominator of the rational expressions. $$\frac{7}{15 x^{2}} \text { and } \frac{13}{24 x}$$

Solve each rational equation. $$\frac{x}{3}=\frac{x}{2}-2$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{2}+\frac{1}{4}}{\frac{1}{2}+\frac{1}{3}}\)

multiply as indicated. $$\frac{4}{x+3} \cdot \frac{x-5}{9}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{7 x}{13}+\frac{2 x}{13}$$

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{5}{2 x}$$

Each exercise is a problem involving motion. You can travel 40 miles on motorcycle in the same time that it takes to travel 15 miles on bicycle. If your motorcycle's rate is 20 miles per hour faster than your bicycle's, find the average rate for each. (TABLE CANNOT COPY)

Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(v\) varies directly as \(r\)

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{11}{3 x}$$

Find the least common denominator of the rational expressions. $$\frac{11}{25 x^{2}} \text { and } \frac{17}{35 x}$$

Solve each rational equation. $$\frac{x}{5}=\frac{x}{6}+1$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{3}+\frac{1}{4}}{\frac{1}{3}+\frac{1}{6}}\)

multiply as indicated. $$\frac{8}{x-2} \cdot \frac{x+5}{3}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{3 x}{17}+\frac{8 x}{17}$$

Each exercise is a problem involving motion. A jogger runs 4 miles per hour faster downhill than uphill. If the jogger can run 5 miles downhill in the same time that it takes to run 3 miles uphill, find the jogging rate in each direction.

Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(w\) varies inversely as \(v\)

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{x}{x-8}$$

Find the least common denominator of the rational expressions. $$\frac{8}{15 x^{2}} \text { and } \frac{5}{6 x^{5}}$$

Solve each rational equation. $$\frac{4 x}{3}=\frac{x}{18}-\frac{x}{6}$$

Simplify complex rational expression by the method of your choice. \(\frac{5+\frac{2}{5}}{7-\frac{1}{10}}\)

Multiply as indicated. $$\frac{x}{3} \cdot \frac{12}{x+5}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{8 x}{15}+\frac{x}{15}$$

Each exercise is a problem involving motion. A truck can travel 120 miles in the same time that it takes a car to travel 180 miles. If the truck's rate is 20 miles per hour slower than the car's, find the average rate for each.

Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(a\) varies inversely as \(b\)

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{x}{x-6}$$

Find the least common denominator of the rational expressions. $$\frac{7}{15 x^{2}} \text { and } \frac{11}{24 x^{5}}$$

Simplify complex rational expression by the method of your choice. \(\frac{1+\frac{3}{5}}{2-\frac{1}{4}}\)

Solve each rational equation. $$\frac{5 x}{4}=\frac{x}{12}-\frac{x}{2}$$

Multiply as indicated. $$\frac{x}{5} \cdot \frac{30}{x-4}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{9 x}{24}+\frac{x}{24}$$

Each exercise is a problem involving motion. In still water, a boat averages 15 miles per hour. It takes the same amount of time to travel 20 miles downstream, with the current, as 10 miles upstream, against the current. What is the rate of the water's current?

In Exercises \(5-8,\) determine the constant of variation for each stated condition. \(y\) varies directly as \(x,\) and \(y=80\) when \(x=4\)

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{13}{5 x-20}$$

Find the least common denominator of the rational expressions. $$\frac{4}{x-3} \text { and } \frac{7}{x+1}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{2}{5}-\frac{1}{3}}{\frac{2}{3}-\frac{3}{4}}\)

Solve each rational equation. $$2-\frac{8}{x}=6$$

Multiply as indicated. $$\frac{3}{x} \cdot \frac{4 x}{15}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{x-3}{12}+\frac{5 x+21}{12}$$

Each exercise is a problem involving motion. In still water, a boat averages 15 miles per hour. It takes the same amount of time to travel 20 miles downstream, with the current, as 10 miles upstream, against the current. What is the rate of the water's current?

Determine the constant of variation for each stated condition. y varies directly as \(x,\) and \(y=108\) when \(x=12\)

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{17}{6 x-30}$$

Find the least common denominator of the rational expressions. $$\frac{2}{x-5} \text { and } \frac{3}{x+7}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{8}+\frac{1}{16}}\)

Solve each rational equation. $$1-\frac{9}{x}=4$$

Multiply as indicated. $$\frac{7}{x} \cdot \frac{5 x}{35}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{x+4}{9}+\frac{2 x-25}{9}$$

Each exercise is a problem involving motion. As part of an exercise regimen, you walk 2 miles on an indoor track. Then you jog at twice your walking speed for another 2 miles. If the total time spent walking and jogging is 1 hour, find the walking and jogging rates.

Determine the constant of variation for each stated condition. \(W\) varies inversely as \(r,\) and \(W=600\) when \(r=10\)