Question 1

A bottle of liquid pool chlorine has a recommended daily dosage of 12 ounces per 10,000 gallons of water. At this rate, how many ounces would be needed in a 22,000 gallon pool?

Accepted Answer

The dosage scales linearly with the volume of water. For 10,000 gallons, 12 ounces are needed, so for 22,000 gallons, it's (22,000 / 10,000) * 12 = 2.2 * 12 = 26.4 ounces.

Question 2

The two triangles pictured below are similar triangles. If side a is 6", side b is 4", and side c is 7.5", find the length of side d.

Accepted Answer

The answer of The two triangles pictured below are similar...

Question 3

A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it takes 3 hours. How long would it take the supervisor working alone?

Accepted Answer

The postal worker can sort the mail in 8 hours, meaning her rate is 1/8 of the mail per hour. Together, they can sort the mail in 3 hours, meaning their combined rate is 1/3 of the mail per hour. To find the supervisor's rate, subtract the worker's rate from the combined rate: 1/3 - 1/8 = 8/24 - 3/24 = 5/24. This means the supervisor can sort the mail alone in 24/5 hours, which is 4 hours and 48 minutes.

Question 4

The ratio of men to women at one college is 4 to 5. If there are 1000 more women than men, how many women are there?

Accepted Answer

The ratio of men to women is 4:5, meaning for every 4 men, there are 5 women. Let the number of men be 4x and the number of women be 5x. According to the problem, 5x = 4x + 1000. Solving for x gives x = 1000. Therefore, the number of women is 5x = 5(1000) = 5000.

Question 5

If 9 is decreased by the reciprocal of a number, the result is $\frac { 7 } { 3 }$. Find the number.

Accepted Answer

Let the number be $ x $. The equation is $ 9 - \frac{1}{x} = \frac{7}{3} $. Solving for $ x $, we get $ \frac{1}{x} = 9 - \frac{7}{3} = \frac{27}{3} - \frac{7}{3} = \frac{20}{3} $. Thus, $ x = \frac{3}{20} $.

Question 6

A kayaker can row 6 miles upstream, against a 2 mph current, in one hour more than he can row 7 miles downstream. What is his average speed in still water?

Accepted Answer

The kayaker's speed in still water can be found by setting up equations based on the given information. Let $x$ be the kayaker's speed in still water. The time to row 6 miles upstream is $ \frac{6}{x-2} $ and the time to row 7 miles downstream is $ \frac{7}{x+2} $. According to the problem, $ \frac{6}{x-2} = \frac{7}{x+2} + 1 $. Solving this equation for $x$ gives $x = 5$ mph.

Question 7

On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit to Cleveland is 170 miles. How far apart are two cities that are 10" apart on this map? Round to the nearest tenth Of a mile.

Accepted Answer

The scale of the map is found by dividing the actual distance by the map distance: 170 miles / 3" = 56.7 miles per inch. For cities 10" apart on the map, the actual distance is 56.7 miles/inch * 10" = 567 miles, rounded to 566.7 miles.

Question 8

A bus driver follows a morning route and an afternoon route each day. Because there are more cities on the morning route, the average speed is 12 miles per hour less than the afternoon route.
She covers 70 miles on the morning route in the same amount of time as she covers 100 miles on the Afternoon route. Find her average speed on the afternoon route.

Accepted Answer

The answer of A bus driver follows a morning route...

Question 9

Nancy shot a 12 on 3 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes? Round to nearest whole number.

Accepted Answer

Nancy's average score per hole is 12 strokes for 3 holes, which is 4 strokes per hole. For 18 holes, her expected score would be 4 strokes/hole * 18 holes = 72 strokes.

Question 10

If 6 is added to the reciprocal of a number, the result is $\frac { 49 } { 8 }$. Find the number.

Accepted Answer

The answer of If 6 is added to the reciprocal...

Question 11

A boat can travel 56 miles upstream against the current in the same amount of time it can travel 84 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current.

Accepted Answer

The answer of A boat can travel 56 miles upstream...

Question 12

Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. What was her Running speed?

Accepted Answer

Let Catherine's running speed be x mph. Then her biking speed is x + 18 mph. Since the time taken for both activities is the same, we have the equation: 3/x = 12/(x + 18). Solving this equation gives x = 6 mph.

Question 13

It takes Terrell 74 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 54 minutes. How long would it take them working together? Round to the nearest tenth of a minute.

Accepted Answer

The answer of It takes Terrell 74 minutes to weed...

Question 14

The recipe for a holiday punch calls for 7 cups of fruit drink and 3 cups of ginger ale. Suppose you want to make as much punch as you can using all of the fruit drink you have, which is 22 cups. How many cups of ginger ale would you need? Round to the nearest tenth of a cup.

Accepted Answer

To maintain the ratio of 7 cups of fruit drink to 3 cups of ginger ale, you set up the proportion 7/3 = 22/x, where x is the amount of ginger ale needed. Solving for x gives x = (3/7) * 22 = 9.4286, which rounds to 9.4 cups.

Question 15

If a baseball player has a batting average of 0.350, his ratio of hits to at-bats 350 to 1000. How many base hits would a player with a batting average of 0.350 have if he had 520 at-bats?

Accepted Answer

A batting average of 0.350 means the player gets 350 hits out of 1000 at-bats. For 520 at-bats, the number of hits is (0.350) * 520 = 182 hits.

Question 16

On August 19, 2002, the ratio of stocks gaining value on the New York Stock Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how many gained? Round to the nearest Whole number.

Accepted Answer

The answer of On August 19, 2002, the ratio of...

Question 17

The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you want to make as much cake batter as you can using all of the flour you have, which is 23 cups. How many cups of Sugar would you need? Round to the nearest tenth of a cup.

Accepted Answer

The answer of The recipe for a sheet cake calls...

Question 18

A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 30 miles per hour. Find the speed of the plane in still air.

Accepted Answer

The speed of the plane in still air can be found by setting up equations based on the given information. Let the speed of the plane in still air be $p$ and the wind speed be $w = 30$ mph. When flying with the wind, the effective speed is $p + w$, and against the wind, it is $p - w$. The time to fly 540 miles with the wind is $540 / (p + 30)$, and the time to fly 480 miles against the wind is $480 / (p - 30)$. According to the problem, the time to fly with the wind is one hour less than the time to fly against it, so we have the equation $540 / (p + 30) + 1 = 480 / (p - 30)$. Solving this equation for $p$ gives us the speed of the plane in still air as 150 miles per hour.

Question 19

In an average year, the ratio of days with rain to dry days in Fort Lauderdale is 26 to 47. How many rainy days are there in an average year?

Accepted Answer

The answer of In an average year, the ratio of...

Question 20

The two triangles pictured below are similar triangles. Find the missing length.

Accepted Answer

The answer of The two triangles pictured below are similar...

Quiz 5: Rational Expressions and Rational Equations

A bottle of liquid pool chlorine has a recommended daily dosage of 12 ounces per 10,000 gallons of water. At this rate, how many ounces would be needed in a 22,000 gallon pool?

A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it takes 3 hours. How long would it take the supervisor working alone?

The ratio of men to women at one college is 4 to 5. If there are 1000 more women than men, how many women are there?

If 9 is decreased by the reciprocal of a number, the result is $\frac { 7 } { 3 }$ . Find the number.

A kayaker can row 6 miles upstream, against a 2 mph current, in one hour more than he can row 7 miles downstream. What is his average speed in still water?

On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit to Cleveland is 170 miles. How far apart are two cities that are 10" apart on this map? Round to the nearest tenth Of a mile.

Nancy shot a 12 on 3 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes? Round to nearest whole number.

If 6 is added to the reciprocal of a number, the result is $\frac { 49 } { 8 }$ . Find the number.

A boat can travel 56 miles upstream against the current in the same amount of time it can travel 84 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current.

Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. What was her Running speed?

It takes Terrell 74 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 54 minutes. How long would it take them working together? Round to the nearest tenth of a minute.

The recipe for a holiday punch calls for 7 cups of fruit drink and 3 cups of ginger ale. Suppose you want to make as much punch as you can using all of the fruit drink you have, which is 22 cups. How many cups of ginger ale would you need? Round to the nearest tenth of a cup.

If a baseball player has a batting average of 0.350, his ratio of hits to at-bats 350 to 1000. How many base hits would a player with a batting average of 0.350 have if he had 520 at-bats?

On August 19, 2002, the ratio of stocks gaining value on the New York Stock Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how many gained? Round to the nearest Whole number.

The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you want to make as much cake batter as you can using all of the flour you have, which is 23 cups. How many cups of Sugar would you need? Round to the nearest tenth of a cup.

A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 30 miles per hour. Find the speed of the plane in still air.

In an average year, the ratio of days with rain to dry days in Fort Lauderdale is 26 to 47. How many rainy days are there in an average year?

The two triangles pictured below are similar triangles. Find the missing length.

Quiz 5: Rational Expressions and Rational Equations

A bottle of liquid pool chlorine has a recommended daily dosage of 12 ounces per 10,000 gallons of water. At this rate, how many ounces would be needed in a 22,000 gallon pool?

The two triangles pictured below are similar triangles. If side a is 6", side b is 4", and side c is 7.5", find the length of side d.

A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it takes 3 hours. How long would it take the supervisor working alone?

The ratio of men to women at one college is 4 to 5. If there are 1000 more women than men, how many women are there?

If 9 is decreased by the reciprocal of a number, the result is 73\frac { 7 } { 3 }37​ . Find the number.

A kayaker can row 6 miles upstream, against a 2 mph current, in one hour more than he can row 7 miles downstream. What is his average speed in still water?

On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit to Cleveland is 170 miles. How far apart are two cities that are 10" apart on this map? Round to the nearest tenth Of a mile.

Nancy shot a 12 on 3 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes? Round to nearest whole number.

If 6 is added to the reciprocal of a number, the result is 498\frac { 49 } { 8 }849​ . Find the number.

A boat can travel 56 miles upstream against the current in the same amount of time it can travel 84 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current.

Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. What was her Running speed?

It takes Terrell 74 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 54 minutes. How long would it take them working together? Round to the nearest tenth of a minute.

The recipe for a holiday punch calls for 7 cups of fruit drink and 3 cups of ginger ale. Suppose you want to make as much punch as you can using all of the fruit drink you have, which is 22 cups. How many cups of ginger ale would you need? Round to the nearest tenth of a cup.

If a baseball player has a batting average of 0.350, his ratio of hits to at-bats 350 to 1000. How many base hits would a player with a batting average of 0.350 have if he had 520 at-bats?

On August 19, 2002, the ratio of stocks gaining value on the New York Stock Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how many gained? Round to the nearest Whole number.

The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you want to make as much cake batter as you can using all of the flour you have, which is 23 cups. How many cups of Sugar would you need? Round to the nearest tenth of a cup.

A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 30 miles per hour. Find the speed of the plane in still air.

In an average year, the ratio of days with rain to dry days in Fort Lauderdale is 26 to 47. How many rainy days are there in an average year?

The two triangles pictured below are similar triangles. Find the missing length.

If 9 is decreased by the reciprocal of a number, the result is $\frac { 7 } { 3 }$ . Find the number.

If 6 is added to the reciprocal of a number, the result is $\frac { 49 } { 8 }$ . Find the number.