Question 1

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-In a certain fraction, the numerator is 3 less than the denominator. If 5 is added to both the numerator and the denominator, the resulting fraction is equal to  . What was the original fraction (not necessarily written in lowest terms)?.
A) 
B) 
C) 
D)

Accepted Answer

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Question 2

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-The numerator of a fraction is 5 times the denominator. If 6 is subtracted from the numerator, and added to the denominator, the resulting fraction is equal to  . What was the original fraction (not written in lowest terms)?.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 3

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-A quantity,  of it,  of it, and  of it, added together, equals 8. What is the quantity?
A) 
B) 
C) 
D)

Accepted Answer

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Question 4

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-Mara can type 1620 words in  hr ( 30 minutes). How many words per minute can she type?
A) 810 words per min
B) 54 words per min
C) 27 words per min
D) 108 words per min

Accepted Answer

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Question 5

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-A machine can fill 1154 boxes of cereal in 0.2 hour. How many boxes of cereal can it fill per hour?
A) 5770 boxes per hr
B) 1154 boxes per hr
C) 3847 boxes per hr
D) 231 boxes per hr

Accepted Answer

To find the number of boxes filled per hour, divide the total boxes filled by the time in hours. 1154 boxes / 0.2 hour = 5770 boxes per hour.

Question 6

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-The winner of the 1998 Peoria 500 (mile) race was Serge Bologna, with an average rate of 174.18 mi per hr. What was his time (to the nearest thousandth of an hour)?
A) 2.919 hr
B) 12.871 hr
C) 2.871 hr
D) 0.18 hr

Accepted Answer

To find the time, divide the total distance by the average speed: Time = Distance / Speed = 500 miles / 174.18 miles per hour = 2.871 hours (to the nearest thousandth).

Question 7

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-The NCAA Division 4 women's champion for the 400-m dash in 1998 was Sally Sprintalot of World State University. Her winning time was 5.06 sec. What was her rate in meters per second?
A) 2024.00 m per sec
B) 77.05 m per sec
C) 81.05 m per sec
D) 79.05 m per sec

Accepted Answer

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Question 8

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 252 mi in the same time that Dana travels 222 mi. If Chuck's rate of travel is 5 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?
A) 42 mph
B) 37 mph
C) 39 mph
D) 45 mph

Accepted Answer

Chuck's speed is 42 mph, derived from the equation based on distance = rate × time, with the given that Chuck's rate is 5 mph more than Dana's.

Question 9

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-The speed of a stream is 5 mph. If a boat travels 62 mi downstream in the same time that it takes to travel 31 mi upstream, what is the speed of the boat in still water?
A) 18 mph
B) 15 mph
C) 10 mph
D) 17 mph

Accepted Answer

The speed of the boat in still water can be found by setting up the equation for time, where time = distance/speed. Let the speed of the boat in still water be x mph. Downstream, the boat's speed is (x + 5) mph, and upstream, it's (x - 5) mph. The time to travel downstream and upstream is the same, so we set the equations equal to each other: 62/(x + 5) = 31/(x - 5). Solving for x gives us 15 mph.

Question 10

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-A plane flies 500 mi with the wind and 300 mi against the wind in the same length of time. If the speed of the wind is 27 mph, what is the speed of the plane in still air?
A) 133 mph
B) 108 mph
C) 113 mph
D) 98 mph

Accepted Answer

The plane's speed in still air is 108 mph. With the wind, the effective speed is 108 + 27 = 135 mph, and against the wind, it is 108 - 27 = 81 mph. The time for both trips is the same: 500/135 = 300/81. Solving this equation confirms the plane's speed in still air is 108 mph.

Question 11

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-Tom Quig traveled 250 mi east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total time of travel was 7 hr, how many miles did he drive at the reduced speed?
A) 40 mi
B) 50 mi
C) 60 mi
D) 35 mi

Accepted Answer

Tom traveled 250 miles in total. Let x be the miles traveled at 10 mph. Then, (250 - x) miles were traveled at 70 mph. The time for the slow part is x/10 hours, and for the fast part is (250-x)/70 hours. The total time is 7 hours: x/10 + (250-x)/70 = 7. Solving this equation gives x = 40 miles.

Question 12

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-A boat goes 320 mi downstream in the same time it can go 240 mi upstream. The speed of the current is  Find the speed of the boat in still water.
A) 40 mph
B) 35 mph
C) 56 mph
D) 30 mph

Accepted Answer

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Question 13

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-A man rode a bicycle for 12 mi and then hiked an additional 8 mi. The total time for the trip was 5 hr. If his biking rate was 10 mph faster than his hiking rate, what was each rate?
A) Biking: 14. mph; hiking: 4.5 mph
B) Biking: 11.5 mph; hiking: 1.5 mph
C) Biking: 12 mph; hiking: 2 mph
D) Biking: 13 mph; hiking: 3 mph

Accepted Answer

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Question 14

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-A boat can go 136 mph in still water. It takes as long to go 720 mi upstream as it does to go downstream 810 mi. How fast is the current?
A) 7 mph
B) 9 mph
C) 8 mph
D) 1 mph

Accepted Answer

The speed of the current can be found by setting up equations based on the distance = speed × time formula for both upstream and downstream. Let the speed of the current be $c$ mph. The speed of the boat upstream is $136 - c$ mph, and downstream is $136 + c$ mph. Since the time taken is the same for both trips, we can set up the equation $\frac{720}{136 - c} = \frac{810}{136 + c}$. Solving this equation for $c$ gives $c = 8$ mph.

Question 15

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-One printer can do a printing job in 11 hr. Another printer can do the same job in 14 hr. How long does it take the two printers to do the job working together?
A) 51  hr
B)  hr
C) 5  hr
D) 6  hr

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 16

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-Martha can rake the leaves in her yard in 2 hr. Her brother can do the job in 3 hr. How long will it take them to do the job working together?
A) 6 hr
B)  hr
C) 1  hr
D)  hr

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 17

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-One maid can clean the house in 7 hr. Another maid can do the job in 4 hr. How long will it take them to do the job working together?
A)  hr
B) 2  hr
C) 9  hr
D)  hr

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 18

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-Frank can type a report in 7 hr. James can type it in 6 hr . How long will it take the two of them working together?
A) 42 hr
B)  hr
C) 3  hr
D)  hr

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 19

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-An experienced accountant can prepare a certain complexity of tax return in 8 hr. A novice accountant can do the job in 11 hr. How long will it take them to do the job working together?
A)  hr
B)  hr
C) 29  hr
D) 4  hr

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 20

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the problem.
-A water tank can be filled in 7 min and emptied in 8 min. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?
A)  min
B) 56 min
C)  min
D) 3  min

Accepted Answer

The answer of Choose the one alternative that best completes...

Quiz 8: Roots and Radicals

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A quantity, of it, of it, and of it, added together, equals 8. What is the quantity?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Mara can type 1620 words in hr ( 30 minutes) . How many words per minute can she type?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A machine can fill 1154 boxes of cereal in 0.2 hour. How many boxes of cereal can it fill per hour?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The winner of the 1998 Peoria 500 (mile) race was Serge Bologna, with an average rate of 174.18 mi per hr. What was his time (to the nearest thousandth of an hour) ?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The NCAA Division 4 women's champion for the 400-m dash in 1998 was Sally Sprintalot of World State University. Her winning time was 5.06 sec. What was her rate in meters per second?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The speed of a stream is 5 mph. If a boat travels 62 mi downstream in the same time that it takes to travel 31 mi upstream, what is the speed of the boat in still water?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A plane flies 500 mi with the wind and 300 mi against the wind in the same length of time. If the speed of the wind is 27 mph, what is the speed of the plane in still air?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A boat goes 320 mi downstream in the same time it can go 240 mi upstream. The speed of the current is Find the speed of the boat in still water.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A man rode a bicycle for 12 mi and then hiked an additional 8 mi. The total time for the trip was 5 hr. If his biking rate was 10 mph faster than his hiking rate, what was each rate?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A boat can go 136 mph in still water. It takes as long to go 720 mi upstream as it does to go downstream 810 mi. How fast is the current?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -One printer can do a printing job in 11 hr. Another printer can do the same job in 14 hr. How long does it take the two printers to do the job working together?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Martha can rake the leaves in her yard in 2 hr. Her brother can do the job in 3 hr. How long will it take them to do the job working together?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -One maid can clean the house in 7 hr. Another maid can do the job in 4 hr. How long will it take them to do the job working together?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Frank can type a report in 7 hr. James can type it in 6 hr . How long will it take the two of them working together?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -An experienced accountant can prepare a certain complexity of tax return in 8 hr. A novice accountant can do the job in 11 hr. How long will it take them to do the job working together?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A water tank can be filled in 7 min and emptied in 8 min. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?