Question 596604
Speed of Joe's boat going upstream = 5 - x where x is the speed of the current
Speed of Joe's boat going downstream = 5 + x

time to go upstream is distance/rate = 36/5-x
time to go downstream is 36/5+x
total time for trip is 40 hours

[36/(5-x)] + [36/(5+x)] = 40

If we multiply both sides of the above equation by (25-x^2)we get:

36(5+x) + 36(5-x) = 40(25-x^2)

Simplify:

180 + 36x + 180 - 36x = 40(25-x^2)
360 = 40(25-x^2)
Divide both sides of the equation by 40
9 = 25 - x^2
x^2 -25 + 9 = 25-x^2-25+x^2
x^2-16=0
x-4=0    x+4=0
x=4      x=-4

The speed of the current is 4 mph.

check:
net speed going upstream is 5-4=1mph  Upstream trip takes 36 hours
net speed going downstream is 5+4=9mph  Upstream trip takes 4 hours
Yotal time = 36 + 4 + 60 hours