Answer
6 minutes
Work Step by Step
If Karen can mow the lawn in $15$ minutes, she can mow $1/15$ of the lawn in $1$ minute. If Kim can mow the lawn in $10$ minutes, she can mow $1/10$ of the lawn in $1$ minute. Together, they can mow $1/15 + 1/10$ of the lawn in $1$ minute. This means they can mow $1/6$ of the lawn in 1 minute. If they can mow $1/6$ of the lawn in 1 minute, they can mow the entire lawn in 6 minutes
