a river rises in the Boston mountains at an altitude of 1250 yards and
after traveling 150 kilometers the river discharges into a lake at an
altitude of 300 meters. What is the overall gradient for the stream in
feet per mile. At one point the river is 16 feet deep and 12 meters
wide. The water has a velocity here of 4 meters per second, what is
the discharge in meters cubed per second?

Hi carlafaye-ga,

This sounds more like an exercise in metric conversion than an exercise in geology!

You need to find the overall gradient in "feet per mile", so I'll
re-phrase the question in those units: "a river rises in the Boston
mountains at an altitude of 3750 feet and after traveling 93.205679
miles the river discharges into a lake at an altitude of 984.25197
feet".

The gradient is therefore (3750 - 984.25197) feet / 93.205679 miles,
which equals 29.6736 feet per mile.

The cross-section of the river is 4.8768 meters (16 feet) times 12
meters, which equals 58.5216 square meters. The discharge is therefore
58.5216 square meters times 4 meters per second, which equals 234.0864
cubic meters per second.

Conversion factors used (from the Linux "units" program):

One yard equals 3 feet
One meter equals 3.2808399 feet
One kilometer equals 0.62137119 miles

Regards,
eiffel-ga