t=(40v)/(v^2-16) where v is the boats speed in km/h and a river current of 4km/h

Question

Jarek lives 20 km upstream from his friend Edward on a river in which the water flows at 4 km/h. If Jarek travels by boat to Edward’s house and back again, the total time, t, in hours, for the round trip is given by the function above. What is the domain if Jarek makes the complete round trip? Explain, please. Graph the function and explain what it shows about the situation. Explain what the behavior of the function near its non-permissible value represents in this context.

Answer 1

20 km stream

water current = 4 kph= v

total time for round trip of 40 km = t(v) = 40v/(v^2-16) = 160/(16-16)= 160/0 = undefined or infinite time to get to the destination going upstream if boat speed = current speed. forever upstream but 20/8 =2.5 hours downstream

boat speed in still water > 4 kph or the boat would never reach the destination upstream, so domain is (4, infinity). Although more realistically, the upper bound should be some finite number, maybe the speed of light, at least.