Question

4. Three workers can do a job in 12 days. One of the workers works twice as fast as each of the
other two. How long would it take the faster worker to do the job alone?​

Answer 1

Is this like direct and inverse variation method

Answer 2

Answer:

The Time taken by slower worker to complete the job alone is 24 days .

Step-by-step explanation:

Given as :

Three workers can do a job in 12 days

One of the workers works twice as fast as each of the  other two

Let the time taken to work done by three worker alone = x , y , y

And The time taken by faster worker =  x

The time taken by slower workers =  y , y

So, According to question

$\dfrac{1}{x}$ + $\dfrac{1}{y}$ +  $\dfrac{1}{y}$  = $\dfrac{1}{12}$

∵ one worker works twice as other two

∴  $\dfrac{1}{x}$  = $\dfrac{2}{y}$                      ..........A

So  $\dfrac{2}{y}$ + $\dfrac{1}{y}$ +  $\dfrac{1}{y}$  = $\dfrac{1}{12}$

Or, $\dfrac{2+1+1}{y}$ = $\dfrac{1}{12}$

Or, $\dfrac{4}{y}$ = $\dfrac{1}{12}$

Or,  $\dfrac{1}{y}$  = $\dfrac{1}{48}$

From eq A

$\dfrac{1}{x}$  = $\dfrac{2}{y}$    

i.e  $\dfrac{1}{x}$  = $\dfrac{2}{48}$

Or,   $\dfrac{1}{x}$ = $\dfrac{1}{24}$

So, Time taken by slower worker = x = 24 days

Hence, The Time taken by slower worker to complete the job alone is 24 days . Answer