identify the type of proportion that the following problems illustrate.then solve the problem
1.A car can travel 210km in 3hours .how far can it travel in 5 hours.
2. Five people can finish painting a wall in 5 hours.if only 2 people are available,how many hours do they have to work to finish the same job?
3.at 65 km/hr,Alfred can reach home in 50 minutes. at what speed should he drive his car so that he can go home 10 minutes earlier
Answer (1)
Answer:Here's the breakdown of each problem, identifying the type of proportion and providing the solution: 1. A car can travel 210km in 3 hours. How far can it travel in 5 hours?Type of Proportion: Direct Proportion. As the time increases, the distance traveled also increases proportionally.Solution: - Find the distance traveled per hour: 210 km / 3 hours = 70 km/hour - Calculate the distance for 5 hours: 70 km/hour * 5 hours = 350 kmAnswer: The car can travel 350 km in 5 hours. 2. Five people can finish painting a wall in 5 hours. If only 2 people are available, how many hours do they have to work to finish the same job?Type of Proportion: Inverse Proportion. As the number of people decreases, the time required to complete the job increases.Solution: - Calculate the total work: 5 people * 5 hours = 25 person-hours (This represents the total amount of work needed) - Divide the total work by the new number of people: 25 person-hours / 2 people = 12.5 hoursAnswer: They would have to work for 12.5 hours. 3. At 65 km/hr, Alfred can reach home in 50 minutes. At what speed should he drive his car so that he can go home 10 minutes earlier?Type of Proportion: Inverse Proportion. As the time to reach home decreases, the speed needs to increase.Solution: - Calculate the total time in minutes: 50 minutes - 10 minutes = 40 minutes (This is the new desired time) - Set up a proportion: (65 km/hr * 50 minutes) = (x km/hr * 40 minutes) - Solve for x: x = (65 km/hr * 50 minutes) / 40 minutes = 81.25 km/hrAnswer: He needs to drive at 81.25 km/hr to reach home 10 minutes earlier.
