Real-Life Math
You are an oil pipeline operator for a company that is moving oil
products from Midville to Smithtown. The towns are 50 miles apart.
The batch you are currently moving contains premium and regular grades of
gasoline.
The premium will go to GasCo and the regular will go to PumpIt.
You are using a computer to operate valves 50 miles away. You must direct
the product so that each of the 2 shippers receives the correct grade of gasoline.
The
line fill (meaning the total number of barrels needed to fill the line) is
1,762. You have already put in 862 barrels. When the line is full, you will
do a batch change.
When you started shipping from Midville, you tested
the gravities of the products. The premium gasoline had a gravity of 81.6
and the regular gasoline had a gravity of 76.6.
By watching your computer
screen, you can watch the gravity of the shipment as it arrives in Smithtown.
The heavier premium will arrive first, then the regular grade.
When
the gravity reaches just the right level, you must cut from GasCo to PumpIt.
That is, you must close 1 valve and open another so that the regular grade
will switch to PumpIt.
Your computer screen shows a picture of all
of your valves. You choose GasCo, then go back to the screen. The valve that
you are going to switch to is flashing. You hit the Cut Button.
The
open green valve (for PumpIt) turns half-green and half-red and starts closing.
The other does the opposite. The regular grade of gasoline is now going to
PumpIt, and GasCo has received its premium grade.
- How many more barrels must go through the line before you do a batch change?
- At what gravity will you cut from GasCo to PumpIt?