How long did it take Misha to finish washing the cars in the following case?Stefan could wash the cars by himself in 6 hours and Misha could wash the cars by himself in 5 hours. Stefan starts...

How long did it take Misha to finish washing the cars in the following case?

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?

Asked on by catd1115

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Stefan requires 6 hours to wash the cars by himself. In one hour he washes 1/6 of the cars. Misha can wash the cars by herself in 5 hours. In 1 hour she can wash 1/5 of the cars.

Stefan has 2.5 hours to wash the cars as he has to go to the football game. In 2.5 hours he has washed (1/6)*2.5 = 5/12 of the cars. This leaves 1 - 5/12 = 7/12 of the cars for Misha to wash. As she washes cars at the rate of 1/5 per hour, it would take her (7/12)/` `(1/5) = (5*7)/12 = 35/12 hours to wash the remaining cars.

35/12 hours is equal to 175 minutes or 2 hours 55 minutes.

Misha finishes washing the cars in 35/12 hours after Stefan leaves.

ksri's profile pic

ksri | High School Teacher | (Level 3) eNoter

Posted on

Stefan could do the whole work in 6 hrs.

Hence in 1 Hr he could finish 1/6 of the work.

Hence in 2.5 Hrs he can finish 2.5/6 of the work =25/60 of the work.

So, when he quits the work in 2.5 hrs. the remaining work =1-25/60

    =35/60 of the work.

Now, Misha can finish the whole work in 5 hrs.

Hence in 1 hr. she can do 1/5 of the work.

Hence she can finish the remaining work of 35/60 in 35/60 divided by 1/5   Hrs.   =  35/60*5/1 hrs =175/60 hrs =2Hrs and 55 mins.

 

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