SOLUTION: Stefan could wash the cars by himself in 6 hours and Misha could wash the cars by himself in 5 hours. Stefan starts washing the cars by himself, but he needs to go to his football

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Stefan could wash the cars by himself in 6 hours and Misha could wash the cars by himself in 5 hours. Stefan starts washing the cars by himself, but he needs to go to his football       Log On


   

Question 884374: Stefan could wash the cars by himself in 6 hours and Misha could wash the cars by himself in 5 hours. Stefan starts washing the cars by himself, but he needs to go to his football game after 2.5 hours. Misha continues the task. How long did it take Misha to finish washing the cars?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What fraction of the cars did Stefan wash in 2.5 hrs?
His rate of washing is:
( 1 job ) / ( 6 hrs ) = +1%2F6+
Note that I call washing all the cars 1 job
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Let +x+ = fraction of cars he washes in 2.5 hrs
+1%2F6+=++x%2F2.5+
Multiply both sides by +6%2A2.5+
+2.5+=+6x+
+x+=+2.5%2F6+
+x+=+5%2F12+
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So, Stefan washes 5/12 of the cars in 2.5 hrs. That
means there are 7/12 of the cars left to wash
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Misha takes over by himself. His rate is:
( 1 job ) / ( 5 hrs ) = +1%2F5+
Let +t+ = time in hrs for him to finish washing cars
by himself
+1%2F5+=+%28+7%2F12+%29+%2F+t+
+1%2F5+=+7%2F%28+12%2At+%29+
Multiply both sides by +5%2A12%2At+
+12t+=+5%2A7+
+t+=+35%2F12+
+t+=+2+%2B+11%2F12+
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How many minutes is +11%2F12+ hrs?
+%2811%2F12%29%2A60+=+55+
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Misha takes 2 hrs and 55 min to finish washing the cars