A Man can do a piece of work in 60 hours. If he takes his Son with him and both work together then the work is finished in 40 hours. How many hours will the son take to do the Same Job, If he worked alone on the job?

A Man can do a piece of work in 60 hours. If he takes his Son with him and both work together then the work is finished in 40 hours. How many hours will the son take to do the Same Job, If he worked alone on the job?

To determine how long the son would take to complete the job if he worked alone, follow the steps.

The man can complete the work in 60 hours.

When both the man and his son work together, they finish the work in 40 hours.

Let's denote the rate at which the man works per hour as 1/60 of the job per hour

When both work together, their combined rate is 1/40 of the job per hour

If the son takes x hours to complete the job alone, his rate would be 1/x of the job per hour.

According to the work formula

Work Rate = Work/Time

1/60 + 1/x = 1/40

Multiply through by 120x to eliminate fractions

2x + 120 = 3x

x = 120

Therefore, if the son worked alone, he would take 120 hours to complete the job.

Work and Time Relationships

In mathematics, work and time relationships involve determining how much work can be completed in a given amount of time, or how long it takes to complete a certain amount of work. This concept is fundamental in fields such as physics, economics, and engineering, where efficiency and productivity are key factors.

Formulas and Equations:

The relationship between work, time, and rate is often expressed using formulas such as

Work = Rate x Time

Here, rate refers to the speed at which work is done per unit of time, and it helps calculate how long it takes to complete a task or how much work can be completed in a specific timeframe.

Significance:

Learning about work and time relationships enhances mathematical reasoning and problem-solving skills. It teaches students how to analyze tasks in terms of efficiency, allocate resources effectively, and make informed decisions based on quantitative data.

Work and time concepts are not limited to mathematics but also extend to fields such as economics (e.g., calculating labor productivity), physics (e.g., determining power output), and biology (e.g., analyzing metabolic rates). Understanding work-time relationships is crucial in practical scenarios.

For example, in project management, estimating project completion times based on team productivity rates is essential. In manufacturing, optimizing production schedules involves calculating how long it takes to manufacture a certain number of products based on production rates.