SOLUTION: kesha and pink can paint a room together in eight hours. if kesha worked alone for three hours and then was joined by pink, the two can complete the job in six more hours. how long

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Question 620122: kesha and pink can paint a room together in eight hours. if kesha worked alone for three hours and then was joined by pink, the two can complete the job in six more hours. how long will it take each person to paint the room?
pls. help me, i tried to answer but i was not able to :(
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
kesha and pink can paint a room together in eight hours.
if kesha worked alone for three hours and then was joined by pink, the two can complete the job in six more hours.
how long will it take each person to paint the room?
:
Let k = time required by K to paint the room alone
Let p = time required by P to do it
Let the completed job = 1 (a painted room)
:
Write an equation for each statement:
:
"kesha and pink can paint a room together in eight hours."
+ = 1
:
"If kesha worked alone for three hours and then was joined by pink, the two can complete the job in six more hours."
K works a total of 9 hrs, P works 6 hrs
+ = 1
:
Combine the two equations, they both = 1
+ = +
Combine like terms
- = -
:
=
cross multiply
p = 2k
:
Use the 1st equation, replace p with 2k
+ = 1
multiply by 2k to get rid of the denominators
2(8) + 8 = 2k
24 = 2k
k = 12 hr for K to paint the room alone
then we know p = 2k, therefore:
2(12) = 24 hrs for P to paint the room alone
:
:
:
Check our solutions in the statement:
"if kesha worked alone for three hours and then was joined by pink, the two can complete the job in six more hours."
+ =
Reduce fractions
+ = 1; confirms our solutions
:
Did I make this understandable to you?