Question

person A can paint the neighbors house 2 times as fast as person B. The year A and B work together, it took them 4 days. How long would it take each to paint the house ?

Answer 1

Person A would take 6 days and Person B would take 12 days.

Step-by-step explanation:

Let $w$ be the work to paint the house.

Let $t_{a}$ be the time taken by person A to do $w$.

Let $t_{b}$ be the time taken by person B to do $w$.

Let $speed_{a}$ be the speed of person A to paint.

Let $speed_{a}$ be the speed of person B to paint.

It is given that person A can paint 2 times as fast as person B.

$speed_{a}=2\times speed_{b}$

So,person B would take twice time as taken by person A.

$t_{b} =2\times t_{a}$

$t_{a}=\frac{w}{speed_{a}}$

$t_{b}=\frac{w}{speed_{b}}$

It is given that both of them would take 4 days to paint the house.

$\frac{w}{speed_{a}+speed_{b}}=\frac{w}{\frac{w}{t_{a}}+\frac{w}{t_{b}}} =\frac{t_{a}\times t_{b}}{t_{a}+t_{b}}$

substituting $t_{b}=2\times t_{a}$

Total time to produce=$\frac{t_{a}\times t_{b}}{t_{a}+t_{b}}=\frac{2\times t_{a}^{2}}{3\times t_{a}} =\frac{2\times t_{a}}{3}=4$

$t_{a}=6$

$t_{b}=2\times t_{a}=2\times 6=12$