Answer:
Time taken by Franklin to shovel alone is 65.5 minutes.
Step-by-step explanation:
Let the time taken by Franklin to shovel alone = x minutes.
Since, the time taken by Angela to shovel = 180 minutes and the time taken by both = 48 minutes.
Then, we have,
Amount of shoveling done in 1 minute by Angela = [tex]\frac{1}{180}[/tex]
Amount of shoveling done in 1 minute by both = [tex]\frac{1}{48}[/tex]
Amount of shoveling done in 1 minute by Franklin= [tex]\frac{1}{x}[/tex]
So, we have,
[tex]\frac{1}{180}+\frac{1}{x}=\frac{1}{48}[/tex]
i.e. [tex]\frac{x+180}{180x}=\frac{1}{48}[/tex]
i.e. [tex]48(x+180)=180x[/tex]
i.e. [tex]48x+8640=180x[/tex]
i.e. [tex]132x=8640[/tex]
i.e. x= 65.5 minutes
Thus, the time taken by Franklin to shovel alone is 65.5 minutes.
