SOLUTION: DAVID CAN WASH A SINK FULL OF DISHES IN 45 MINUTES, WHILE TODD CAN WASH THE SAME AMOUNT IN 30 MINUTES. HOW LONG WILL IT TAKE THEM TO WASH THE DISHES IF THEY DO IT TOGETHER ?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: DAVID CAN WASH A SINK FULL OF DISHES IN 45 MINUTES, WHILE TODD CAN WASH THE SAME AMOUNT IN 30 MINUTES. HOW LONG WILL IT TAKE THEM TO WASH THE DISHES IF THEY DO IT TOGETHER ?      Log On


   

Question 1019883: DAVID CAN WASH A SINK FULL OF DISHES IN 45 MINUTES, WHILE TODD CAN WASH THE SAME AMOUNT IN 30 MINUTES. HOW LONG WILL IT TAKE THEM TO WASH THE DISHES IF THEY DO IT TOGETHER ?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
DAVID CAN WASH A SINK FULL OF DISHES IN 45 MINUTES, 
David's dishwashing rate is 1 sinkful per 45 minutes or

matrix%281%2C2%2C1%2CSINKFUL%29%2Fmatrix%281%2C2%2C45%2CMINUTES%29 or matrix%281%2C2%2C1%2F45%2CSINKFUL%2FMINUTE%29

WHILE TODD CAN WASH THE SAME AMOUNT IN 30 MINUTES.
Todd's dishwashing rate is 1 sinkful per 30 minutes or

matrix%281%2C2%2C1%2CSINKFUL%29%2Fmatrix%281%2C2%2C30%2CMINUTES%29 or matrix%281%2C2%2C1%2F30%2CSINKFUL%2FMINUTE%29

HOW LONG WILL IT TAKE THEM TO WASH THE DISHES IF THEY DO IT TOGETHER ?
Suppose it takes them x minutes working together.

Then their combined dishwashing rate is 1 sinkful per x minutes or

matrix%281%2C2%2C1%2CSINKFUL%29%2Fmatrix%281%2C2%2Cx%2CMINUTES%29 or matrix%281%2C2%2C1%2Fx%2CSINKFUL%2FMINUTE%29

The equation comes from:

matrix%283%2C1%2C%22DAVID%27S%22%2CDISHWASING%2CRATE%29%22%22%2B%22%22matrix%283%2C1%2C%22TODD%27S%22%2CDISHWASING%2CRATE%29%22%22=%22%22matrix%284%2C1%2CTHEIR%2CCOMBINED%2CDISHWASING%2CRATE%29

1%2F45%2B1%2F30=1%2Fx

Solve that for x.

Edwin