Question

Going against the current, a boat takes 6 hours to make a 120-mile trip. When the boat travels with the current on the return trip, it takes 5 hours.

If x = the rate of the boat in still water and y = the rate of the current, which of the following systems could be used to solve the problem?

Answer 1

'Let speed of boat in still water = x mph
& speed of current or stream = y mph
Downstream speed = x + y
Upstream speed = x - y
Using the relation , distance = speed x time, we get,
3(x + y) = 24 or, x + y =8
4(x - y) = 16 or, x - y =4
Solving the system of equations simultaneously, we get,
x = 6, y= 2
Rate of current = 2 mph, rate of boat in still water = 6 mph'

~Sources~ https://www.wyzant.com/resources/answers/78697/finding_current_and_rate_of_boat_in_still_water

Answer 2

You want:

\(5(x + y) = 120\)

and

\(6(x - y) = 120\)