Question

How long would it take franklin to shovel the driveway alone?

Answer 1

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 = $\frac{1}{180}$

Amount of shoveling done in 1 minute by both = $\frac{1}{48}$

Amount of shoveling done in 1 minute by Franklin= $\frac{1}{x}$

So, we have,

$\frac{1}{180}+\frac{1}{x}=\frac{1}{48}$

i.e. $\frac{x+180}{180x}=\frac{1}{48}$

i.e. $48(x+180)=180x$

i.e. $48x+8640=180x$

i.e. $132x=8640$

i.e. x= 65.5 minutes

Thus, the time taken by Franklin to shovel alone is 65.5 minutes.