If 3 people take 2 hours to complete a job. how long will it take 4 people?

Question

Problem drom text book and we do not understand how they got the solution of 1.5 hours

Answer 1

This is a problem which involves a process called inverse variation. As the number of people go up, the time goes down proportionately.

 

The general formula for inverse variation is

 

x*y = k K being a constant.

 

So for example, if the area of a rectangle is 72sq ft. what are the possible dimensions. I'm going to stick to just the whole numbers, although fractions work too.

 

1 by 72 

2 by 36

3 by 24

4 by 18

and others.

 

If you compare each to 1 by 72, do you see one got doubled and the other got divided b y 2 to get 2 by 36.

Or 1 by 72 got multiplied by 3 in one column while being divided by 3 in the second column to get 3 by 24.

 

Another example is for motion problems.

 

Let's say I have to travel 12 miles.

rate * time = distance

1mph * 12 hours = 12

2mph * 6 hours = 12

3mph * 4 hours = 12

 

Same scenario as the previous problem.

 

So if 3 people can do a job in 2 hours, that means 6 hours of work is to be done. If that 6 hours of work is now divided among 4 people, it will take 1.5 hours.

 

In terms of the formula

x*y=K

2*3=K

6 =K

x*y=6

4*y=6

y=1.5.

 

Hope this helped.