### All Algebra II Resources

## Example Questions

### Example Question #212 : Equations

Jason has $ and spends $ a day. Paul has $ and adds $ a day. When will they have the same amount of money?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

represent time it will take for them to have the same amount of money. By adding on both sides, subtracting on both sides later, and finally dividing by on both sides, we get days.

### Example Question #213 : Equations

A cat can dig a hole at a rate of feet per day. This cat starts digging for one week. A dog comes along and watches the cat dig and joins along. The dog digs for feet per day. If a buried treasure is feet below surface, how long has the cat dug until they both reach the trasure?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

represents the cat's head start and how much the cat started digging. The last part represents the sum of the rates of both animals since they start working together. is the number of days.

Subtract on both sides.

Divide on both sides.

days

Our answer is not done since it's asking about the cat. So we add and to get days.

### Example Question #213 : Equations

A cat can dig a hole at a rate of feet per day. This cat starts digging for one week. A dog comes along and watches the cat dig and joins along. The dog digs for feet per day. If a buried treasure is feet below surface, how long has the cat dug until they both reach the trasure?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

represents the cat's head start and how much the cat started digging. The last part represents the sum of the rates of both animals since they start working together. is the number of days.

Subtract on both sides.

Divide on both sides.

days

Our answer is not done since it's asking about the cat. So we add and to get days.

### Example Question #214 : Equations

To convert Celsius to Fahrenheit temperatures, you multiply Celsius by and then add . What is the Celsius temperature when the Fahrenheit temperature is ?

**Possible Answers:**

**Correct answer:**

Our equation looks like: By subtituting , we have Subtract on both sides.

Multiply on both sides.

### Example Question #215 : Equations

A lion spots a deer meters away. The lion chases the deer at meters/second. At the same time, the deer runs away at a speed of meters/second. How long will it take when the two animals are meters apart?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

As time passes, the deer has the head start and its distance will be . Since the lion's rate is faster and we want the differences of their distances traveled, we subtract the distance the deer went and lion's distance which is .

Subtract on both sides. Since is greater than and is negative, our answer is negative. We treat as a subtraction problem.

Divide on both sides. When dividing with another negative number, our answer is positive.

seconds

### Example Question #215 : Equations

A lion spots a deer meters away. The lion chases the deer at meters/second. At the same time, the deer runs away at a speed of meters/second. How long will it take when the two animals are meters apart?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

As time passes, the deer has the head start and its distance will be . Since the lion's rate is faster and we want the differences of their distances traveled, we subtract the distance the deer went and lion's distance which is .

Subtract on both sides. Since is greater than and is negative, our answer is negative. We treat as a subtraction problem.

Divide on both sides. When dividing with another negative number, our answer is positive.

seconds

### Example Question #216 : Equations

Ellen is swimming in the ocean meters from the beach. She screams for help and starts swimming towards the shore at a speed of meters/second. Twenty seconds later, Joe starts rowing a boat toward her at a rate of meters/second. How far has Joe rowed when he meets Ellen?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

Ellen has the head start which is represented by . Then, Ellen and Joe go at different rates but at the same time which is represented by . represents time.

Subtract on both sides.

Divide on both sides.

Then we need to multiply that by since we are looking for the distance Joe went. Our answer is or miles.

### Example Question #217 : Equations

Ellen is swimming in the ocean meters from the beach. She screams for help and starts swimming towards the shore at a speed of meters/second. Twenty seconds later, Joe starts rowing a boat toward her at a rate of meters/second. How far has Joe rowed when he meets Ellen?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

Ellen has the head start which is represented by . Then, Ellen and Joe go at different rates but at the same time which is represented by . represents time.

Subtract on both sides.

Divide on both sides.

Then we need to multiply that by since we are looking for the distance Joe went. Our answer is or miles.

### Example Question #218 : Equations

Joe and Cara are making meatballs. They have to make. Joe can make meatballs a minute while Cara can make meatballs a minute. After working together for forty-two minutes, Cara had to leave leaving Joe to finish the rest. How long does Joe take to finish the rest?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

represents how many meatballs they make together

represents the number of meatballs Joe needs to make with being time

Subtract on both sides.

Divide on both sides.

minutes

### Example Question #81 : Solving Equations

A tank can fill a swimming pool in two hours. A hose can fill the same swimming pool in three hours. How long will it take in hours if both the tank and hose fill the swimming pool at the same time?

**Possible Answers:**

**Correct answer:**

Let's set-up an equation.

represents the time they will take together and represents the job both the tank and hose finish as a whole

Find the common denominator and add the fractions. . Cross-multiply.

Divide on both sides.

hours