# Charles can shovel the snow off his driveway in 40 minutes. He shovels for 20 minutes and then is joined by Joaney. If they shovel the remaining snow in 10 minutes, how long would it have taken Joaney to shovel the driveway alone?

##### 1 Answer

So Joaney would take 40 minutes to complete the task on their own.

Very full explanation given.

#### Explanation:

Let the amount of 'work' to complete the job be

Let the work rate of Charles be

Let the work rate of Joaney be

Let generic designation of time be

Let time Charles works be

Let the time Joaney works be

We have the relationship

Set

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Charles works on his own for the initial time of 20 minutes giving:

He is then joined by Joaney and they work together for 10 minutes more. So the above becomes

Using

Make everything have a common denominator of 4

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So Joaney would take 40 minutes to complete the task on their own.