Jackson can remove the shingles off of a house in 7 hours, while Martin can remove the shingles in 5 hours. How long will it take them to remove the shingles if they work together?

Accepted Solution

Answer: [tex]2\ hours\ and\ 55\ minutes[/tex]Step-by-step explanation: WE can use the following formula: [tex]\frac{T}{A}+\frac{T}{B}=1[/tex] Where "T" is the time time working together, "A" the time for person A working alon and "B" is the time for person B working alone. Based on the data given in the exercise, we can identify that: [tex]A=7\\B=5[/tex] Therefore, substituting these values into the formula and solving for "T", we get that this is: [tex]\frac{T}{7}+\frac{T}{5}=1\\\\\frac{12T}{35}=1\\\\T=(1)(\frac{35}{12})\\\\T=2.9167\ hours[/tex] Since 1 hour has 60 minutes: [tex](0.9167h)(\frac{60min}{1h})=55min[/tex] Therefore, if they work together, it will take them 2 hours and 55 minutes to remove the shingles.