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PRESENTATION: SOLVING LINEAR EQUATIONS

Nenotte Aminata Yacine Seck

Created on April 27, 2023

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Transcript

SOLVING A DISTANCE, TIME AND RATE PROBLEM USING LINEAR EQUATIONS

NENOTTE AMINATA YACINE SECK MATH 100 - 01 MARCH 19, 2023

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WHY THIS TOPIC?

A better understanding of relationships between two or more variables

As a student majoring in Management, linear equations could be useful in financial planning such as identifying earning potential, determining variable costs & break-even point, budgeting etc.

HISTORICAL FACTS

  • LINEAR EQUATIONS

TERMS & DEFINITIONS

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear' equation.

APPLICATION

Alex and Anna want to meet at a holiday cottage. Alex leaves his house on a scooter at 80 km/h. Anna leaves 5 hours later driving a car to catch up with Alex travelling at 180 km/h. How long will it take Anna to catch up with Alex?

RESULTS

We know the relation between distance, time and rate is given by Distance = Rate x Time. Let t represent the number of hours that Alex has spent driving.

Next

1. CREATE A TABLE

Therefore, we get:

  • D1 = 80* t = 80t
  • D2 = 180 * t-5 = 180 ( t-5 )

The distance travelled by both is the same. So, the equation to be solved is : 80t = 180 ( t-5 )

Next

2. Distribute 80t = 180 ( t-5 ) We obtain 80t = 180t – 900

Next

3. REGROUP THE LIKE TERMS

80t = 180t – 900 80t – 180t = -900 -100t = -900

Next

4. ISOLATE t AND SOLVE

-100t = -900 t= -900 / -100 t = 9 hours

Next

5. PLUG IN t INTO (t-5)

If t = 9, t-5 = 9 - 5 t- 5 = 4 hours

Next

ANSWER

Alex travelled for 9 hours. Anna needs to travel for 4 hours to catch up with him.

References

- (n.d.). Retrieved from – https://www.math.utah.edu/~gustafso/s2010/FTC-Method-of-Quadrature.pdf

- (n.d.). Retrieved from - https://www.cuemath.com/algebra/linear-equations/

- (n.d.). Retrieved from - https://www.vedantu.com/question-answer/who-discovered-speed-class-9-physics-cbse-6011a6b463ac962acb70e03b

THANK YOU !

Esto es un párrafo listo para contener creatividad, experiencias e historias geniales.