We have the old machine that last 27 1/2 = 27.5 minutes to wash a load.
If the new machine takes 10% longer, it will take 27.5 minutes plus the 10% of 27.5 minutes, that is 0.10 * 27.5 = 2.75 minutes.
We can then add and get: 27.5 + 2.75 = 30.25 mnutes.
Other way to think about it is that aquantity y that is 10% bigger than quantity x, can be calculated as y=(1+0.10)x=1.1x.
In this case, x=27.5 and y = 1.1 * 27.5 = 30.25.
The new machine takes 30.25 minutes to wash the load.