Question

Mario and kenneth work at car station.the time that mario take is washing car alone is 20 minutes less than the time that kenneth takes in washing the same car.if both of them work together in washing the car,it will take them 90 minutes.how long will it take each of them to wash the car?
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Answer 1

Given :  time that mario take is washing car alone is 20 minutes less than the time that kenneth takes in washing the same car.

both of them work together in washing the car,it will take them 90 minutes.

To Find : how long will it take each of them to wash the car

Solution:

Let say Kenneth wash car  in   K minutes   K > 20

Mario wash car in K  - 20  Minute

Kenneth work in 1  minute  = 1/K

Mario work in 1 minute  = 1/(K - 20)

Together their work in 1 minute = 1/K  + 1/(K - 20)

Together they complete work in 90 minutes

Hence 1 min work = 1/90

1/K  + 1/(K - 20) = 1/90

=> 90 ( K - 20  + K )  = K ( K - 20)

=> 90 (2K - 20)  = K² - 20K

=> 180K - 1800 = K² - 20K

=> K²  - 200K + 1800 = 0

K = (200 ± √32800 )/2

=> K = 190.55 min , 9.45 min    ignores the Value less than 20

Hence  Kenneth wash car  in  190.55  minutes    

Mario wash car in 170.55  Minute

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