by AuSmith » Thu Mar 12, 2009 11:09 am
There are a few assumptions:
1) The potatoes have the same density
2) The [unparseable or potentially dangerous latex formula] in. and [unparseable or potentially dangerous latex formula] in. potatoes have the same shape. You could even assume they are cubes if you wanted, with [unparseable or potentially dangerous latex formula] in long meaning [unparseable or potentially dangerous latex formula] in. on a side.
3) She peels skin at a constant rate.
The key is that she is peeling the surface of the potatoes. You want to find how much more/less surface area the [unparseable or potentially dangerous latex formula] in. potatoes have compared to the [unparseable or potentially dangerous latex formula] in. ones.
First find how many [unparseable or potentially dangerous latex formula] in. potatoes she has compared to the [unparseable or potentially dangerous latex formula] in. ones. The [unparseable or potentially dangerous latex formula] inchers have [unparseable or potentially dangerous latex formula] more volume, and hence [unparseable or potentially dangerous latex formula] more weight per potato. Divide [unparseable or potentially dangerous latex formula] to sort of normalize, then divide that by [unparseable or potentially dangerous latex formula]. Call [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula] inchers should have [unparseable or potentially dangerous latex formula] more surface area, and take that much longer to peel. So, 44 minutes times how many more potatoes and times how much longer they take to peel.
[unparseable or potentially dangerous latex formula]?
Or... you can work an equivalent problem:
If you have a collection of [unparseable or potentially dangerous latex formula] in. cubes that total [unparseable or potentially dangerous latex formula] cubic inches and a collection of [unparseable or potentially dangerous latex formula] inch cubes that total [unparseable or potentially dangerous latex formula] cubic inches, how much more total surface area does the collection of [unparseable or potentially dangerous latex formula] inch cubes have?
You have [unparseable or potentially dangerous latex formula] small potatoes with [unparseable or potentially dangerous latex formula] sq. inches apiece. That's [unparseable or potentially dangerous latex formula] total square inches.
You have [unparseable or potentially dangerous latex formula] big potatoes with [unparseable or potentially dangerous latex formula] sq. inches apiece. That's [unparseable or potentially dangerous latex formula] total square inches.
Treat [unparseable or potentially dangerous latex formula] minutes as another unit of surface area. Then, it will take [unparseable or potentially dangerous latex formula] minutes to peel the big potatoes.