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Pete and Pam are planning to paint a house together. Pete thinks it would take him 2 times as long as it would take Pam to paint the entire house. Working together, they can complete the job in 18 hours. How long will it take each of them, working alone to complete the job?

 Feb 21, 2021
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Call Pam's  rate  1 / x     where x  is the  hrs Pam takes by herself

Call Pete's rate   1 / (2x)     where 2x is the hrs Pete takes by himself  

 

Rate  * time  =  whole job done  ....so...

 

(1/x)((18)  +  1/  (2x) * 18  = 1

 

18/x   +  18/ (2x)    = 1

 

18/x   +  9/x  = 1

 

[ 18  + 9 ]   / x   =  1

 

27   =   x  =    no. of hours  that Pam takes  by herself

 

2(x)  = 2(27)   = 54  =  no. of  hours that Pete takes by himself

 

 

cool cool cool

 Feb 21, 2021

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