Direction: Solve the given and write whetherHIS DIRECT PROPORTIONPROPORTION.огTauesse INUERSEA family wentontheirand reachedif they willhome120kmtravelwill they be?forSa trip. they travelled foraway from their home.hours, how far away2 hoursAromA groupcertainof constructionroad.workersare asked to palish afcan finishLuili6 menIt takelo menthe soldto Anish Job?Job1030 days, how longGa workersworkerstocan build a wall inbuild the same wall10 days, how long will it takeAt acertainISspeed of60 kph acan takes 20 minutes to travel adistance. at what speed must it travel this distance if itto take only is minutes?5) A carpenter receivesPhD 680should hereceives for 6 hoursfor8 hours of work. How muchor work at the same rater6) Sarah uses #14 bananas to bake 3 loaves of banana bread.how many loaves of bread can she bake if she uses42 bananas.
Answer (1)
Answer:Analyzing the ProportionsProblem 1: Family Trip * Direct Proportion: As the travel time increases, the distance traveled also increases. * Equation: Distance = Speed * Time * Solution: Distance = 120 km / 2 hours = 60 km/hour. If they travel for 5 hours, Distance = 60 km/hour * 5 hours = 300 km.Problem 2: Construction Workers * Inverse Proportion: As the number of workers increases, the time to complete the job decreases. * Equation: Work = Rate * Time (where Rate is the work done by one worker per day) * Solution: Work = 6 men * 30 days = 180 man-days. If there are 10 men, Time = 180 man-days / 10 men = 18 days.Problem 3: Building a Wall * Inverse Proportion: As the number of workers increases, the time to complete the job decreases. * Equation: Work = Rate * Time * Solution: Work = 10 men * 10 days = 100 man-days. If there are 8 workers, Time = 100 man-days / 8 men = 12.5 days.Problem 4: Traveling a Distance * Inverse Proportion: As the speed increases, the time to travel a distance decreases. * Equation: Distance = Speed * Time * Solution: Time = Distance / Speed. If the speed is 60 kph and the time is 20 minutes (1/3 hour), Distance = 60 kph * (1/3 hour) = 20 km. To travel this distance in 15 minutes (1/4 hour), Speed = Distance / Time = 20 km / (1/4 hour) = 80 kph.Problem 5: Carpenter's Earnings * Direct Proportion: As the hours worked increase, the earnings increase. * Equation: Earnings = Hourly Rate * Hours Worked * Solution: Hourly Rate = ₱680 / 6 hours = ₱113.33/hour. If he works 8 hours, Earnings = ₱113.33/hour * 8 hours = ₱906.64.Problem 6: Baking Banana Bread * Direct Proportion: As the number of bananas increases, the number of loaves increases. * Equation: Loaves = Bananas / Bananas per Loaf * Solution: Bananas per Loaf = 14 bananas / 3 loaves = 4.67 bananas/loaf. If she uses 42 bananas, Loaves = 42 bananas / 4.67 bananas/loaf ≈ 9 loaves.
