Respuesta :
givenAnalyzing the information given in the exercise, you can identify that you can use the following Work rate formula:
[tex]\frac{t}{t_A}+\frac{t}{t_B}=1[/tex]Where:
- The individual time for object A is:
[tex]t_A[/tex]- The individual time for object B is:
[tex]t_B[/tex]- And the time for object A and object B is:
[tex]t[/tex]In this case, let be the time (in hours) the experienced window washer can wash all the windows in Mike's house:
[tex]t_A=2[/tex]And let be the time (in hours) the new trainee can wash all the windows:
[tex]t_B=7[/tex]Knowing these values, you can substitute them into the formula and solve for "t":
[tex]\begin{gathered} \frac{t}{2}+\frac{t}{7}=1 \\ \\ \frac{7t+2t}{14}=1 \\ \\ 7t+2t=1\cdot14 \\ \\ 9t=14 \\ \\ t=\frac{14}{9} \end{gathered}[/tex]Dividing the numerator by the denominator, you get:
[tex]t\approx1.556[/tex]This time is in hours, but you have to express the answer in hours and minutes. So you need to remember that:
[tex]1h=60\min [/tex]So, in order to convert from hours in Decimal form to hours and minutes, you need to:
- Rewrite the time as follows:
[tex]1h+0.556h[/tex]- Convert the Decimal number from hours to minutes:
[tex](0.556h)(\frac{60\min}{1h})=33.36\min [/tex]- Since there are 60 seconds in 1 minute:
[tex](0.36\min )(\frac{60\sec}{1\min})=21.6\sec [/tex]Then:
[tex]t=1hour,33\text{ }minutes\text{ }and\text{ }21.6\text{ }seconds[/tex]Therefore, rounded to the nearest minute, you get that the answer is:
[tex]t=1\text{ }hour\text{ }and\text{ }33\text{ }minutes\text{ }[/tex]