SOLUTION: After a snowstorm ken and beteena clear their drive way. ken can clear the snow by himself in four hours beteena can clear the snow in five.after beteena has been working for two h

Algebra ->  Rate-of-work-word-problems -> SOLUTION: After a snowstorm ken and beteena clear their drive way. ken can clear the snow by himself in four hours beteena can clear the snow in five.after beteena has been working for two h      Log On


   

Question 732453: After a snowstorm ken and beteena clear their drive way. ken can clear the snow by himself in four hours beteena can clear the snow in five.after beteena has been working for two hours ken is able to join her. how much longer will it take them working together to remove the rest of the snow?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Beteena can clear the snow in five hrs.
In 2 hrs, working alone, she can clear
+2%2F5+ of the driveway.
That means +3%2F5+ is left to clear.
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Add their rates of working to get rate
working together.
( 1 driveway / 4 hrs ) + ( 1 driveway / 5 hrs ) = ( 3/5 d.w. / t hrs )
+1%2F4+%2B+1%2F5+=+%283%2F5%29+%2F+t+
+1%2F4+%2B+1%2F5+=+3+%2F+%285t%29+
Multiply both sides by +20t+
+5t+%2B+4t+=+12+
+9t+=+12+
+t+=+4%2F3+
1 hr plus 1/3 of an hr is
1 hr and 20 min
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check:
+1%2F4+%2B+1%2F5+=+%283%2F5%29+%2F+t+
+1%2F4+%2B+1%2F5+=+%283%2F5%29+%2F+%284%2F3%29+
+5%2F20+%2B+4%2F20+=+%283%2F5%29%2A%283%2F4%29+
+9%2F20+=+9%2F20+
OK