Question

An experienced window washer can wash all the windows in Mike’s house in 2 hours, while a new trainee can wash all the windows in 7 hours. How long would it take them working together? Round your answer to the nearest minute if needed.Provide your answer below:t=____hours and_____minutes

Answer 1

givenAnalyzing the information given in the exercise, you can identify that you can use the following Work rate formula:

`(t)/(t_A)+(t)/(t_B)=1`

Where:

- The individual time for object A is:

`t_A`

- The individual time for object B is:

`t_B`

- And the time for object A and object B is:

`t`

In this case, let be the time (in hours) the experienced window washer can wash all the windows in Mike's house:

`t_A=2`

And let be the time (in hours) the new trainee can wash all the windows:

`t_B=7`

Knowing these values, you can substitute them into the formula and solve for "t":

`\begin{gathered} (t)/(2)+(t)/(7)=1 \\ \\ (7t+2t)/(14)=1 \\ \\ 7t+2t=1\cdot14 \\ \\ 9t=14 \\ \\ t=(14)/(9) \end{gathered}`

Dividing the numerator by the denominator, you get:

`t\approx1.556`

This time is in hours, but you have to express the answer in hours and minutes. So you need to remember that:

`1h=60\min`

So, in order to convert from hours in Decimal form to hours and minutes, you need to:

- Rewrite the time as follows:

`1h+0.556h`

- Convert the Decimal number from hours to minutes:

`(0.556h)((60\min)/(1h))=33.36\min`

- Since there are 60 seconds in 1 minute:

`(0.36\min )((60\sec)/(1\min))=21.6\sec`

Then:

`t=1hour,33\text{ }minutes\text{ }and\text{ }21.6\text{ }seconds`

Therefore, rounded to the nearest minute, you get that the answer is:

`t=1\text{ }hour\text{ }and\text{ }33\text{ }minutes\text{ }`