Question 1

A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 14 minutes. How long does it take to fill the tub if both faucets are open? Give the answer in minutes.

Accepted Answer

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

Question 2

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 3

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

Accepted Answer

The answer of One number is 3 times as large...

Question 4

A water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 4 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 5

An airplane flying against the wind travels 380 miles in the same amount of time it would take the same plane to travel 400 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 6

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)3 mph
D)1 mph
E)6 mph

Accepted Answer

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

Question 7

A water tank can be filled in 28 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 8

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 9

If  is added to twice the reciprocal of a number, the result is 2. Find the number.

Accepted Answer

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

Question 10

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 11

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)21 minutes
C)24 minutes
D)25 minutes
E)26 minutes

Accepted Answer

Let's denote the amount of water that fills the sink in one minute as "x", and the amount of water that drains out of the sink in one minute as "y".
We know that:
x = 1/6 (since it takes 6 minutes to fill the sink)
y = 1/8 (since it takes 8 minutes to empty the sink)
When both the faucet and the drain are open, the net amount of water that enters the sink each minute is:
x - y = 1/6 - 1/8 = 1/24
Therefore, the amount of time it takes the sink to overflow is:
1 / (x - y) = 1 / (1/24) = 24 minutes

So, the best choice is C) 24 minutes.

Question 12

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 13

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)40 minutes
D)18 minutes
E)9 minutes

Accepted Answer

Let the capacity of the sink be 40 units (which can be any unit of volume like liters, gallons, etc.). The faucet can fill 4 units per minute (40 units in 10 minutes) and the drain can empty 5 units per minute (40 units in 8 minutes). 
When both the faucet and the drain are open, the net inflow of water is 4-5=-1 units per minute, which means the sink will be emptied at the rate of 1 unit per minute. 
Therefore, it will take 40/1=40 minutes to empty the sink. 
So, the correct answer is choice C, 40 minutes.

Question 14

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

Accepted Answer

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

Question 15

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

Let the volume of the bathtub be 1 unit (we can assume any unit) 
The cold water faucet fills the bathtub in 15 minutes, that means it fills 1/15 of the bathtub in 1 minute. 
The hot water faucet fills the bathtub in 18 minutes, that means it fills 1/18 of the bathtub in 1 minute. 
When both faucets are open, the volume of water filled in one minute is (1/15 + 1/18) units. 
Simplifying, (1/15 + 1/18) = 0.2 + 0.16 = 0.36. 
Therefore, the time taken to fill the bathtub when both faucets are open is (1/0.36) minutes 
= 2.7777... minutes, which is approximately equal to 2.78 minutes. 
Therefore, the best choice is B.

Question 16

To train for the running of a triathlon, Jerri jogs 1 hour each day over the same 7-mile course. Four miles of the course is downhill, whereas the other 3 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 17

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

Accepted Answer

The answer of Tina is training for a biathlon. To...

Question 18

A bathtub can be filled by the cold water faucet in 10 minutes and by the hot water faucet in 11 minutes. The drain can empty the tub in 4 minutes. Can the tub be filled if both faucets and the drain are open?
A)No
B)Yes

Accepted Answer

The cold water faucet fills 1/10 of the tub per minute, and the hot water faucet fills 1/11 of the tub per minute. Together, they fill 1/10 + 1/11 = 21/110 of the tub per minute. The drain empties 1/4 of the tub per minute. The net rate is 21/110 - 1/4 = -23/220, meaning the tub will be emptied, not filled.

Question 19

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

Accepted Answer

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

Question 20

The numerator of a certain fraction is 1 more than the denominator. If  is added to the fraction, the result is 2. Find the fraction.

Accepted Answer

The answer of The numerator of a certain fraction is...

Quiz 7: Rational Expressions

A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 14 minutes. How long does it take to fill the tub if both faucets are open? Give the answer in 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

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

A water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 4 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open? __________ minutes

An airplane flying against the wind travels 380 miles in the same amount of time it would take the same plane to travel 400 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 water tank can be filled in 28 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?

If is added to twice the reciprocal of a number, the result is 2. Find the number.

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

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?

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

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 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 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 bathtub can be filled by the cold water faucet in 10 minutes and by the hot water faucet in 11 minutes. The drain can empty the tub in 4 minutes. Can the tub be filled if both faucets and the drain are open?

The numerator of a certain fraction is 1 more than the denominator. If $The numerator of a certain fraction is 1 more than the denominator. If is added to the fraction, the result is 2. Find the fraction.$ is added to the fraction, the result is 2. Find the fraction.