Problems requiring logical reasoning

Question

Two workers complete a 9-hour workday, working together. The first worker, working alone, completes the work in 12 hours. For how many hours does the second worker completes the job?

Answer 1

Since $\frac{1}{9}-\frac{1}{12}=\frac{1}{36}$, it'd take $36$ hours, which is a long "workday".

Answer 2

Use the classic speed=distance/time formula which implies that distance= speed$\times$time. In this case, 'distance' is the work that they complete.

Let $P_{1}$ = person 1 and $P_{2}$ = person 2, and let $W$ be the work they have to complete which is a constant. We are given:

$W = (P_{1}+P_{2})\times 9$

$W = P_{1} \times 12$

We want to find $W$ in terms of $P_{2}$ alone.

$ W = 9P_{1} + 9P_{2} \implies P_{1} = \frac{W - 9P_{2}}{9} $.

Putting this in our second equation for $W$ gives

$W = \frac{12W - 108P_{2}}{9} => 108P_{2} = 3W => W = P2 \times 36$

So it takes Person 2 $36$ hours to complete the work.