Expressions Of Pj Problems
Row Your Boat

Row Your Boat

You can row a boat at 6 miles/hr in a given river when the water is still. You plan to row upstream for 12 miles and back when the river's current flows at 2 miles/hr. How long will the entire trip take (ignore time it takes to change direction)?

The string: S7P5A51 (physical change - duration ).
{mi} = {you, boat, paddle, river}
Si = the boat's containership (i.e. the boat contains you, paddle, etc); the river's containership (i.e. the river contains the boat).
Independent Pj Problem (IPP): river's containership
Dependent Pj Problems (DPP): change (speed of boat), motion (distance covered by boat).
Pj Problem of Interest (PPI) is change (the change in time measured as the difference between starttime and endtime of roundtrip). Time (duration) problems are usually change problems.
The math:
Row Your Boat
Figure 1.1 illustrates the upstream and downstream speed of boat. When boat is moving upstream, it is slowed by the rivers current.
So, its speed = 6 - 2 = 4 miles/hr.
So time it takes to travel 12 miles upstream = 12/4 = 3 hrs.
When boat is moving downstream, it is aided by rivers current
So, its speed = 6 + 2 = 8 miles/hr.
So time it takes to travel 12 miles downstream = 12/8 = 3/2 = 1.5 hrs.
Set starttime, t0 = 0 hrs'
So duration of roundtrip (upstream then downstream) = 4.5 hrs.


The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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