# Algebra II : Solving Equations

## 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?

Explanation:

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?

Explanation:

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

### 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?

Explanation:

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

### 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 ?

Explanation:

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?

Explanation:

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?

Explanation:

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?

Explanation:

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?

Explanation:

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?

Explanation:

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?