ACTIVITY 3: Variations in Real Life!
Directions: Determine if what kind of variation each situation illustrates. Explain your answer.
1. Marie's salary depends on the number of hours she has to work, if she works 8 hours a day her daily rate would be P400.00. If she will work longer, she will get a higher pay.
2. 48 men can do a piece of work in 24 days, while 36 men complete the same work in 32 days. The fewer the worker, the longer to finish the job.
3. From home to work with a distance of 80 km, it will take Marco 2 hours to travel if his average speed is 40km/hr. If he will speed up to 60 km/hr, it will only take him 1.5 hours to travel.
4. The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of students working on the solutions. It takes 36 minutes for students to solve 18 problems.
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Verified answer
Answer:
Situation 1: Marie's salary depends on the number of hours she works, and as she works more hours, she earns a higher pay. This situation illustrates a direct variation. When the number of hours worked increases, the salary increases proportionally. It can be expressed as P = kh, where P is the salary, h is the number of hours worked, and k is a constant representing the rate of pay per hour.
Situation 2: The time it takes to complete a piece of work varies inversely with the number of men working on the job. This situation illustrates an inverse variation. As the number of workers decreases, the time required to complete the work increases. It can be expressed as W = k/m, where W is the time in days, m is the number of men, and k is a constant representing the work rate.
Situation 3: Marco's travel time varies inversely with his speed. As he increases his speed, the travel time decreases. This situation also illustrates an inverse variation. It can be expressed as T = k/v, where T is the time in hours, v is the speed in km/hr, and k is a constant.
Situation 4: The time needed to solve an exercise set of variation problems varies directly with the number of problems and inversely with the number of students working on the solutions. This is a combination of direct and inverse variation. The more problems there are, the more time it takes, and the fewer students there are, the more time each student needs to solve the problems. It can be expressed as T = (kp)/s, where T is the time in minutes, p is the number of problems, s is the number of students, and k is a constant.
Step-by-step explanation:
In each situation, the relationship between the variables (such as salary, time, or work rate) can be described using mathematical equations for direct or inverse variation. Understanding the type of variation is essential for solving problems and making predictions in these scenarios.
Answer:
1. Marie's salary: Direct variation
2. Number of men and time to complete work: Inverse variation
3. Marco's travel time and speed: Direct variation
4. Minutes needed to solve problems: Combination of direct and inverse variation