Question

Person A can paint the neighbor's house 6 times as fast as Person B. The year A and B worked together it took them 4 days. How long would it take each to paint the house?

Answer 1

Person A will take 4,67 days

Person B will take 28 days

Explanation:

They both paint the house in 4 days, then in one day they will paint 1/4 of the house.

Let call "x " number of days person B takes to paint neighbor´s house, and in one day B will paint 1/x

Then person A would take x/6 to paint the same house, and in one day A will paint 1/x/6 or 6/x

According problem statement they both A and B took 4 days painting the house, therefore

1/x + 6/x = 1/4

( 1 + 6 ) /x = 1 /4

( 1 + 6 )*4 = x

7*4 = x

x = 28 days

So person B would take 28 days

And person A would take 28/6 or 4,67 days

Answer 2

Person A takes 4.66 days and person B 28 days

Explanation:

Let t = time required by A to paint the house

"Person A can paint the neighbor's house 6 times faster than Person B."

Thus:

6 * t = time required by person B

Therefore we have to:

4 / t + 4/6 * t = 1

we solve:

(4 * 6 * t + 4 * t) 6 * t * t = 1

(28 * t) 6 * t * t = 1

6/28 = t

t = 14/3

that is, person A takes 4.66 days and person B 28 days (4.66 * 6)