How to find a percent

Question

Please help! 2 people working together paint the outside of a house in 6 hours. Working alone but at the same rate the first person can paint the outside of a house in 14 hours. What percent of the outside of the house can the 2nd painter paint when two people work together?

Answer 1

the first person paints the house in 14 hours

the first person does 1/14 of the house in one hour

together they paint the house in six hours

the first person does 6/14 of the house when working with the second person

the first person does 6/14=3/7 of the house so the second person must do the rest which is 4/7 of the house

4/7=0.571428571428571428=57.143% or 57 1/7 % is done by the second person

by the way it takes the second person 10.5 hours working alone

(1/14)(6)+(1/y)(6)=1

(6/14)+(6/y)=1

(3/7)+(6/y)=1

3y+42=7y

42=4y

y=10.5 hours

Answer 2

Let x = number of hours it takes the 2nd person to do the job alone

 

1/x = amount done by 2nd person each hour

1/14 = amount done by first person each hour

1/6 = amount done by both per hour when they work together

 

1/14 + 1/x = 1/6

 

Multiply by the LCD, 42x, to get 3x + 42 = 7x

 

                                                    4x = 42

 

                                                      x = 10.5 hours

 

Percent done by second painter = (1/10.5 /hour)(6 hours)(100) = 57.1%