Question

. Mari and Liam can each wash a car and vacuum its interior in 2 hours. Zach needs 3 hours to do this same job alone. If Zach, Liam, and Mari work together, how long will it take them to clean a car?

Answer 1

It will take 45 mins to wash a car when Zach, Liam, and Mari work together.

Explanation:

Given:

Time required for Mari to wash a car = 2 hours

Time required for Liam to wash a car = 2 hours

Time required for Zach to wash a car = 3 hours

We need to find the time required to wash a car when Zach, Liam, and Mari work together.

Solution:

Let the time required to wash a car by all three of them be 'x'.

Now first we will find the rate.

Rate is given by Number of job completed divided by time required to complete the job.

Rate of Mari =
`(1)/(2)`

Rate of Liam =
`(1)/(2)`

Rate of Zach =
`(1)/(3)`

Rate when all three work together =
`(1)/(x)`

Now we can say that;

Rate when all three work together is equal to sum of Rate of Mari, Rate of Liam, Rate of Zach.

framing in equation form we get;

`(1)/(2)+\frac12+\frac13=\frac1x\\\\(1+1)/(2)+\frac13=\frac1x\\\\(2)/(2)+\frac13=\frac1x\\\\1+\frac13=\frac1x`

Now we will take the LCM to make the denominator same we get;

`(3)/(3)+\frac13=\frac1x\\\\(3+1)/(3)=\frac1x\\\\\frac43=\frac1x`

Now using cross multiplication we get;

`x=\frac34\ hrs`

Now we know that;

1 hour = 60 mins

`\frac34\ hrs` = Number of minutes in
`\frac34\ hrs`

using Unitary method we get;

Number of minutes in
`\frac34\ hrs` =
`60 * \frac34 = 45 \ mins`

Hence it will take 45 mins to wash a car when Zach, Liam, and Mari work together.