Question

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

Answer 1

Time taken by Franklin to shovel alone is 65.5 minutes.

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 =
`(1)/(180)`

Amount of shoveling done in 1 minute by both =
`(1)/(48)`

Amount of shoveling done in 1 minute by Franklin=
`(1)/(x)`

So, we have,

`(1)/(180)+(1)/(x)=(1)/(48)`

i.e.
`(x+180)/(180x)=(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.