39 Persons Can Repair a Road in 12 Days, Working 5 Hours a Day. in How Many Days Will 30 Persons, Working 6 Hours a Day, Complete the Work?

Road repair efficiency analysis: Understand the time it takes for 39 people working 5 hours daily to repair a road in 12 days, then calculate how many days it will take for 30 workers operating 6 hours each day to finish the job.

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

It will take approximately 13 days for 30 persons, working 6 hours a day, to complete the work.

To solve this problem, we can use the concept of man-hours, which represents the total amount of work done by all workers combined.

Given:

• 39 persons can repair the road in 12 days, working 5 hours a day.
• We want to find out how many days it will take for 30 persons, working 6 hours a day, to complete the work.

First, let's calculate the total man-hours required to repair the road based on the first scenario: Total man-hours = (number of persons) × (hours worked per day) × (number of days) Total man-hours = 39 persons × 5 hours/day × 12 days

Now, let's find out the total man-hours available in the second scenario: Total man-hours = 30 persons × 6 hours/day × number of days

Since the amount of work done is the same in both scenarios, we can set the two expressions for total man-hours equal to each other:

39 × 5 × 12 = 30 × 6 × number of days

Now, let's solve for the number of days:

39 × 5 × 12 = 30 × 6 × number of days

→ 2340 = 180 × number of days

→ number of days = 2340 / 180

→ number of days ≈ 13

So, it will take approximately 13 days for 30 persons, working 6 hours a day, to complete the work.

Direct Proportion and Inverse Proportion

Direct proportion and inverse proportion are two types of relationships between two quantities.

1. Direct Proportion: In direct proportion, as one quantity increases, the other quantity also increases, and vice versa. This means that if you double one quantity, the other also doubles. Mathematically, two quantities, x and y, are in direct proportion if their ratio is constant. It can be represented as: y=kx Where k is the constant of proportionality. For example, if you're driving at a constant speed, the distance you travel is directly proportional to the time you spend driving. If you double your speed, you'll double the distance traveled in the same amount of time.

2. Inverse Proportion: In inverse proportion, as one quantity increases, the other quantity decreases, and vice versa. Mathematically, two quantities, x and y, are in inverse proportion if their product is constant. It can be represented as: xy=k Where k is the constant of proportionality. For example, if you're painting a wall and you increase the number of painters, the time it takes to paint the wall decreases. Here, the number of painters and the time taken are inversely proportional.

To summarize:

• In direct proportion, if one quantity increases, the other increases as well, and if one quantity decreases, the other decreases too.
• In inverse proportion, if one quantity increases, the other decreases, and vice versa.