math problem!!!?

Question

Christopher can paint the interior of his house in 15 hours. if he hires cynthia to help him, they can do the same job together in 9 hours. if he lets cynthia work alone, how long will it take her to paint the interior of his house?

I know the answer- 22.5 hours. . but please explain how you get that answer!!!

Answer 1

Christopher can paint the interior of his house in 15 hours

Christopher and cynthia can paint the interior of his house in 9 hours

in one hour chris paints 1/15 of the job

in nine hours he will have painted 9/15 of the job so that means that in nine hours cynthia will have painted 6/15 of the job or 0.4

to get how long it takes her to finish the job you say she painted 0.4 of the job in 9 hours so
9/.4 = 22.5hours

another way to look at it is that .4 = 40%

so this means that she could only do 40% of the job in 9 hours now you need to find how long it will take her to 100% if the job

Answer 2

let r be the helper's rate

Christopher can paint his house in 15 hrs, then in 1 hr, he can paint 1/15 of the house so his rate is 1/15

given that with the help of the helper, they can finish the job in 9 hrs. That means how much of the house he can paint in 9 hrs plus how much of the house the helper can paint in the same amount of time will equal to 100% of the house

(1/15)(9) + 9r = 1
9r = 2/5
r = 2/45

so the rate of the helper is 2/45 of the house in 1 hr.

(2/45)t = 1
t = 22.5 hrs <== answer

hope this helps!

Answer 3

Suppose the total area to be painted = x square units.
Chris can paint x/15 sq. units in 1 h
Chris + Cynthia can paint x/9 sq. units in 1 h.
So, in 1h Cynthia alone paints (x/9) - (x/15) sq. units.
= (5x-3x)/45 = 2x/45

For completing 2x/45 sq. units, Cynthia takes 1 h. So for completing, x sq. units, Cynthia will take
x/(2x/45) = 45/2 = 22.5 h.

Answer 4

treat this problem as a distance-time problem....

so lets say the "distance" of the house is x

the speed at which Chris paints is thus x/15 (dis/time= speed)

and the speed at which they both TOGETHER paint, is x/9

so logically, the speed at which Cynthia paints is (x/9)-(x/15), right? (as speed of both Chris and Cynthia - speed of Chris = speed of Cynthia)

so Cynthia's speed = (x/9) - (x/15) = (2x/45)

now distance/speed = time (we know the distance is x) hence:

hence x/(2x/45) = Cynthia's time

hence Cynthia's time = 45x/2x = 22.5 hours. proven