What is the speed of the current?

Question

A Barge moves 11 km/h in still water. It travels 21 km up river and 21 km down river in a total time of 22hr. What is the speed of the current.

Answer 1

21 = (11+k)*t = 11t + kt

21 = (11-k)*(22-t) = 242 - 11t - 22k + kt

11T + kT = 242 - 11T - 22k + kT

11T = 242 - 11T - 22k

22T = 242 - 22k

T = 11 - k

21 = (11 + k)(11-k)

21 = 121 - k^2

0 = 100 - k^2

k = 10 <-- negatives not allowed

T = 11-k = 11-10 = 1

upstream: speed is 11+10 = 21, for 1 hour travel

downstream speed is 11-10 = 1 , so 21 hours needed.

total travel time is 22 hours