LEOV Word Problems Topic Practice #2

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At Barton High School this year, 45 students are taking Japanese. That number has been increasing at a rate of 3 students per year. The number of Barton students who are taking German this year was 108, and this number has been decreasing at a rate of 4 students per year.

Assuming this trend continues, which of the equations below could help you find how many years it will take before the number of students taking Japanese equals the number taking German?

• $45+3x=108+4x$

• $45x+3=108x+4$

• $45+3x=108-4x$

• $45x+3=108x-4$

Solve the equation you found in the previous problem. Assume that “this year” refers to 2013. In what year will the number of Barton students taking Japanese equal those taking German? [Hint: Read this question carefully. The final answer is not “9”]

The next set of questions will use the following information, so write it down carefully: A herd of elephants began moving at a speed of 6 miles per hour. One lone elephant stayed behind. Two hours later, it decided to catch up with the herd and began moving at a speed of 10 miles per hour.

Let "t" = time that has passed the herd started moving.

Type "done" in the box below when you have copied this information.

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Which of these expressions correctly represents the time that has passed since the lone elephant started moving?  

•  $x-2$  

•  $2-x$  

•  $2x$  

•  $\frac{x}{2}$  

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Use your answer to the previous problem. Which of these equations could help you find how long it took the long elephant to catch up to the herd?

• $6\left(2-x\right)=10x$

• $6\left(2x\right)=10x$

• $10\left(x-2\right)=6x$

• $10\left(\frac{x}{2}\right)=6x$

Solve the equation you found in the previous problem to answer the following: For how long has the herd been moving when the loan elephant catches up to it?

How long has the lone elephant been moving when it catches up with the herd?

How far had the herd traveled when the elephant caught up with it?

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Two friends, Sally and Teresa, live 70 miles apart. They decide to ride their motorbikes to meet each other. Fortunately, there is a single straight road which connects their two houses. 

Sally starts from her house and heads East a speed of 20 mph. Teresa starts from her house and heads West at 15 mph. Which equation below could help you find how long it will take them before they meet? 

•  $20t-15t=70$  

•  $20\left(t-70\right)=15t$  

•  $20t=70-15t$  

•  $15\left(t-70\right)=20t$  

How long does it take the two friends to meet?