Write a function for a stream word problem.

Question

The river flows at 1.5 meters per second.

Write a rational function rule for the total time required to travel a distance d downstream and back in a river flowing at a rate v_r

Answer 1

the speed of the current is 1.5

the speed of the boat is V

downstream with the current the speed is V+1.5

upstream against the current the speed is V-1.5

d = r * t, so t = d/r

the total time is d/(V+1.5) + d/(V-1.5)

= [d(V-1.5) + d(V+1.5) ] / (V^2 - 2.25)

= 2dV / (V^2 - 2.25)

In general, if the speed of the current changes, as suggested in the statement of the problem

for speed of the boat V and speed of the current V_r the formula becomes

T ( d,V,V_r) = 2 d V / ( V^2 - V_r ^ 2)