Length and Distance

Work, Age and Distance Word Problems (Applications of Quadratic Equations)

Prepare: Pen and Paper for Notes

Lesson Goals:

• Review of Number and Geometry Word Problems

• Another Solution solving Geometry Problems

• Solve Age, Work and Distance Word Problems

• Practice Exercises

Review

Practice Exercise on Solving Number Problems

Fill in the Blank

Review #1 (LM 31 Math Exercise #8 p.13)

The product of two numbers is 18 and their sum is 9. Find the numbers.

(Separate your answers with a comma, and no spacing).

Fill in the Blank

Review #2 (LM 19 Math Exercise #9 p.13)

The length of a rectangular tarpaulin is 3 feet more than thrice its width and its area is 126 square feet. What is the length of the tarpaulin?

(No spacing. Include the unit).

Fill in the Blank

Review #3 (additional item)

A rectangular table has an area of $$27\ ft^2$$ and  a perimeter of 24 ft. What are the dimensions of the table?

(Separate your answer with a comma, and no spacing. Include the unit at the end.)

end of review

Next Slide: Solving Work Problems

Solving Work Problems

Don't forget to watch the Recording on Applications of Quadratic Equations (check Help Center channel)

Remember:

• Work is the product of force and distance

• Rate is the reciprocal of the time a person finished the job

• A work done is equivalent to one

• The time spent working together is ideally shorter than doing the job alone.

Fill in the Blank

Practice Exercise #1 (LM 31 Math Exercise #11, p.13)

Kenneth and Mario work in a carwash station. The time that Mario takes in washing a car alone is 60 minutes less than the time that Kenneth takes in washing the same car. If both of them work together in washing the car it will take them 72 minutes. How long will it take each of them to wash the car?

(Write your answer following Kenneth then Mario's time respectively. Separate them with comma, no spacing. Include unit.)

Fill in the Blank

Practice Exercise #2 (additional item)

Two pipes are working together can fill a tank in 35 minutes. If the large pipe alone can fill the tank in 24 minutes less than the time taken by the smaller pipe. Find the time taken by each pipe.

(Write your answer following Small pipe then Large pipe's time respectively. Separate them with comma, no spacing. Include unit.)

Solving Age Problems

Remember

• Be familiar on how to represent past, present and future ages

• Be familiar with the use of verbs that may serve as clue in translating a problem into an equation (e.g. His age was…- meaning past age)

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Practice Exercise #3 (LM 31 Math Exercise #10)

Marilyn is 3 years younger than her friend Rosie. In 7 years, the product of their ages will be thrice the product of their ages 5 years ago. How old are they at present?

(Write your answer following Rosie then Marilyn's time respectively. Separate them with comma, no spacing.)

Fill in the Blank

Practice Exercise #4 (LM 31 Math Exercise #20, p.14)

Leonor is twice as old as her sister Marl. The quotient of their ages five years ago was seven less than Marl’s present age. Find their present ages.

(Write your answer following Marl then Leonor's time respectively. Separate them with comma, no spacing.)

Solving Distance Problems

Remember:

• Distance is the product of rate and time.

• Be familiar with different cases of distance problems – round trip, object moving in the same direction (overtaking) and moving in different directions

Fill in the Blank

Practice Exercise #5 (LM 31 Math Exercise #12, p.13)

Monique drives her car for 300 kilometers at a certain average speed. If she were to drive the car 10 kilometers per hour more than that speed, the trip would be 1 hour less. Find the current speed of the car.

(Include the unit.)

end

Prepare to answer Activity 2 (check LM 31) next meeting.