Related Rates - Rowing and Running
Author: Jamie Mulholland

text here

optimal traveller

red traveller

black traveller

Total Distance

Elapsed Time
   (hours)

totaltimeoptimal = 2.1165151389911676
Popt = (0.8728715609439696, 0)
t1optimal = 1.091089451179962
O = Intersect(yAxis, xAxis)
B = Point(xAxis)
a = Segment(O, B)
P = Point(a)
runpath = Segment(P, B)
t_2: runpath / 5
A = Point(yAxis)
rowpath = Segment(A, P)
t_1: rowpath / 2
totaltime: t_1 + t_2
T = 0.1 (slider from 0 to 3.3, step 0.01)
f_2 = If(x < t1optimal, x(A) + x / t1optimal * (x(Popt) - x(A)), If[x < totaltimeoptimal, x(Popt) + (x(B) - x(Popt)) * (x - t1optimal) / (totaltimeoptimal - t1optimal), 6])
g_2 = If(x < t1optimal, y(A) * (1 - x / t1optimal), 0)
currenttime: T totaltime
g = If(x < t_1, y(A) * (1 - x / t_1), 0)
f = If(x < t_1, x(A) + x / t_1 * (x(P) - x(A)), If[x < totaltime, x(P) + (x(B) - x(P)) * (x - t_1) / (totaltime - t_1), 6])
totaldistance: rowpath + runpath
b = CurveCartesian(f(t), g(t), t, 0, T)
Q: (f(T), g(T))
T3: "time = " + T + "   hours"
T4: " = " + totaldistance
T5: totaltime + ""
Q_2: (f_2(T), g_2(T))
b_2 = CurveCartesian(f_2(t), g_2(t), t, 0, T)
c = false
T9: rowpath + " + " + runpath
T10: T + ""
T11: T + ""
T12: totaltimeoptimal + ""
rowpathoptimal = Segment(A, Popt)
runpathoptimal = Segment(Popt, B)
totaldistanceoptimal: rowpathoptimal + runpathoptimal
T2: rowpathoptimal + " + " + runpathoptimal
T13: " = " + totaldistanceoptimal