Question 1

A bathtub can be filled by the cold water faucet in 7 minutes and by the hot water faucet in 12 minutes. How long does it take to fill the tub if both faucets are open? Give the answer in minutes.

Accepted Answer

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Question 2

The numerator of a certain fraction is 5 more than the denominator. If  is added to the fraction, the result is 3. Find the fraction.

Accepted Answer

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Question 3

One number is 3 times as large as another. The sum of their reciprocals is  . Find the two numbers.

Accepted Answer

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Question 4

Travis paddles his kayak in the harbor at Morro Bay, California, where the incoming tide has caused a current in the water. From the point where he enters the water, he paddles 2 miles against the current, then turns around and paddles 2 miles back to where he started. His average speed when paddling with the current is 2 miles per hour faster than his speed against the current. If the complete trip (out and back) takes him 1.5 hours, find his average speed when he paddles against the current.
A) 2 mph
B) 4 mph
C) 1 mph
D) 3 mph
E) 6 mph

Accepted Answer

The answer of Travis paddles his kayak in the harbor...

Question 5

Graph  and  on the same coordinate system. At what points do the two graphs intersect?
A) 
B) 
C) 
D)

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The answer of Graph  and  on the same...

Question 6

A bathtub can be filled by the cold water faucet in 15 minutes and by the hot water faucet in 18 minutes. How long does it take to fill the tub if both faucets are open?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A bathtub can be filled by the...

Question 7

Travis paddles his kayak in the harbor at Morro Bay, California, where the incoming tide has caused a current in the water. From the point where he enters the water, he paddles 4 miles against the current, then turns around and paddles 4 miles back to where he started. His average speed when paddling with the current is 6 miles per hour faster than his speed against the current. If the complete trip (out and back) takes him 1.4 hours, find his average speed when he paddles against the current. __________ miles per hour

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Question 8

An airplane flying against the wind travels 390 miles in the same amount of time it would take the same plane to travel 410 miles with the wind. If the wind speed is a constant 10 miles per hour, how fast would the plane travel in still air? __________ miles per hour

Accepted Answer

The answer of An airplane flying against the wind travels...

Question 9

A sink can be filled by the cold water faucet in 6 minutes. The drain can empty a full sink in 8 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow?
A) 27 minutes
B) 26 minutes
C) 24 minutes
D) 25 minutes
E) 21 minutes

Accepted Answer

The cold water faucet fills the sink at a rate of 1/6 sink per minute, and the drain empties it at a rate of 1/8 sink per minute. The net rate of filling is 1/6 - 1/8 = 1/24 sink per minute. Therefore, it will take 24 minutes to fill the sink.

Question 10

If  is added to twice the reciprocal of a number, the result is 1. Find the number.

Accepted Answer

The answer of If  is added to twice the...

Question 11

Tina is training for a biathlon. To train for the running portion of the race, she runs 5 miles each day, over the same course. The first 2 miles of the course is on level ground, while the last 3 miles is downhill. She runs 2 miles per hour slower on level ground than she runs downhill. If the complete course takes 1 hour, how fast does she run on the downhill part of the course? __________ miles per hour

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Question 12

A bathtub can be filled by the cold water faucet in 17 minutes and by the hot water faucet in 18 minutes. The drain can empty the tub in 14 minutes. Can the tub be filled if both faucets and the drain are open?
A) No
B) Yes

Accepted Answer

The rate at which the cold water faucet fills the tub is 1/17 of the tub per minute. The rate at which the hot water faucet fills the tub is 1/18 of the tub per minute. The rate at which the drain empties the tub is 1/14 of the tub per minute. 
Therefore, the combined rate of both faucets filling the tub is 1/17 + 1/18 = 35/306 of the tub per minute. 
At the same time, the drain is emptying the tub at a rate of 1/14 of the tub per minute. 
To determine if the tub can be filled, we need to compare the combined rate of the faucets filling the tub to the rate at which the drain is emptying the tub. 
35/306 is greater than 1/14, so the tub can be filled if both faucets and the drain are open.

Question 13

A boat travels 28 miles up the river in the same amount of time it takes to travel 52 miles down the same river. If the current is 3 miles per hour, what is the speed of the boat in still water? d r t Upstream Downstream __________ miles per hour

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The answer of A boat travels 28 miles up the...

Question 14

A water tank can be filled in 27 hours by an inlet pipe and emptied in 36 hours by an outlet pipe. How long will it take to fill the tank if both pipes are left open? __________ hours

Accepted Answer

The answer of A water tank can be filled in...

Question 15

Graph  and  on the same coordinate system. At what points do the two graphs intersect?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph  and  on the same...

Question 16

The sum of a number and its reciprocal is  . Find the number.

Accepted Answer

The answer of The sum of a number and its...

Question 17

To train for the running of a triathlon, Jerri jogs 1 hour each day over the same 9-mile course. Five miles of the course is downhill, whereas the other 4 miles is on level ground. Jerri figures that she runs 2 miles per hour faster downhill than she runs on level ground. Find the rate at which Jerri runs on level ground. __________ miles per hour

Accepted Answer

The answer of To train for the running of a...

Question 18

A water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 6 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open? __________ minutes

Accepted Answer

The answer of A water faucet can fill a sink...

Question 19

A sink can be filled by the cold water faucet in 3 minutes. The drain can empty a full sink in 6 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow? __________ minutes

Accepted Answer

The answer of A sink can be filled by the...

Question 20

A water faucet can fill a sink in 10 minutes, whereas the drain can empty it in 8 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?
A) 10 minutes
B) 80 minutes
C) 18 minutes
D) 40 minutes
E) 9 minutes

Accepted Answer

The answer of A water faucet can fill a sink...

Quiz 6: Reducing Rational Expressions to Lowest Terms

A bathtub can be filled by the cold water faucet in 7 minutes and by the hot water faucet in 12 minutes. How long does it take to fill the tub if both faucets are open? Give the answer in minutes.

The numerator of a certain fraction is 5 more than the denominator. If $The numerator of a certain fraction is 5 more than the denominator. If is added to the fraction, the result is 3. Find the fraction.$ is added to the fraction, the result is 3. Find the fraction.

One number is 3 times as large as another. The sum of their reciprocals is . Find the two numbers.

Graph and on the same coordinate system. At what points do the two graphs intersect?

A bathtub can be filled by the cold water faucet in 15 minutes and by the hot water faucet in 18 minutes. How long does it take to fill the tub if both faucets are open?

An airplane flying against the wind travels 390 miles in the same amount of time it would take the same plane to travel 410 miles with the wind. If the wind speed is a constant 10 miles per hour, how fast would the plane travel in still air? __________ miles per hour

A sink can be filled by the cold water faucet in 6 minutes. The drain can empty a full sink in 8 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow?

If is added to twice the reciprocal of a number, the result is 1. Find the number.

A bathtub can be filled by the cold water faucet in 17 minutes and by the hot water faucet in 18 minutes. The drain can empty the tub in 14 minutes. Can the tub be filled if both faucets and the drain are open?

A boat travels 28 miles up the river in the same amount of time it takes to travel 52 miles down the same river. If the current is 3 miles per hour, what is the speed of the boat in still water? d r t Upstream Downstream __________ miles per hour

A water tank can be filled in 27 hours by an inlet pipe and emptied in 36 hours by an outlet pipe. How long will it take to fill the tank if both pipes are left open? __________ hours

Graph and on the same coordinate system. At what points do the two graphs intersect?

The sum of a number and its reciprocal is . Find the number.

A water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 6 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open? __________ minutes

A sink can be filled by the cold water faucet in 3 minutes. The drain can empty a full sink in 6 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow? __________ minutes

A water faucet can fill a sink in 10 minutes, whereas the drain can empty it in 8 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?