Basic Arithmetic : Linear Equations with Time

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #1 : Linear Equations With Time

It takes Sarah  minutes to gather all the materials she needs to do her math homework. It also takes Sarah  minutes to do  algebra problems. If Sarah starts her homework at  and has  algebra problems to complete, what time will she finish her algebra homework?

Possible Answers:

Correct answer:

Explanation:

We can write a linear equation from the information given in the question:

Since Sarah has 15 problems, she has 3 sets of 5 problems.

Substituting that information gives the following equation:

Now, the question asks at what time Sarah will finish her algebra problems.

Now, add that to 3 pm.

Example Question #2 : Linear Equations With Time

It takes Daisy  hour to plant  strawberry plants. If her goal is to plant  strawberry plants, how many hours will she need to spend planting?

Possible Answers:

Correct answer:

Explanation:

Let  equal the number of hours it takes Daisy to plant strawberry plants.

Given that she can plant 10 strawberry plants in an hour, Daisy can plant  strawberry plants in an hour.

If she wants to plant 70 strawberry plants, then she will plant  strawberry plants.

Dividing both sides by 10, we find that Daisy will take  to plan 70 strawberry plants. 

Example Question #3 : Linear Equations With Time

Two joggers start from the opposite end of a  mile course running toward each other. The first jogger is running at a rate of  miles per hour, while the second jogger is running at a rate of  miles per hour. After how many hours will the joggers meet?

Possible Answers:

Correct answer:

Explanation:

Let  represent the number of hours each jogger runs. We know that the first jogger is running at a rate of 4 miles per hour; since , we therefore know that the first jogger runs a distance of .

By the same logic, we know that the second jogger runs a distance of 

Since we are looking for the point at which the joggers meet up after running from opposite directions, we know that together they will have covered a total of 10 miles. Therefore:

Simplifying the equation:

Example Question #4 : Linear Equations With Time

Jimmy the handyman earns  an hour for fixing bathrooms. If he earned  in a day, how many hours did he work? 

Possible Answers:

Correct answer:

Explanation:

Let  equal the total number of hours Jimmy works in a given day. If he earns $30 per hour, then  is the total amount of money Jimmy earns in a day. Given that he earned $270 on a given day:

Dividing both sides by 30:

Example Question #5 : Linear Equations With Time

Francine wakes up at am every day to get to school, and she always arrives at am.  If it takes Francine  minutes to get ready, how long does it take her to get to school?

Possible Answers:

 hour,  minutes

 hours

 hours,  minutes

 hour,  minutes

 hour,  minutes

Correct answer:

 hour,  minutes

Explanation:

To solve this problem, you need to create a linear equation. First, you know that it takes two hours total for Francine to get to school. Two hours can also been translated into a hundred and twenty minutes. Second, you know that it only takes her twenty minutes to get ready.  Your variable is the time it takes her to get to school.

 

So: 

Therefore, .

Now we convert this back into hours and minutes.

Since 60 minutes is 1 hour it takes Francine an hour and fourty minutes to get to school. 

 

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