A tugboat goes 160 miles upstream in 10 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without a current and the speed of the current.

Question

radar · Answer

Let x = the current speed.
Let b = boat speed. 
Remember d=st (distance equals speed times time)
160 = 10(b-x) and
160 = 5 (b+x) now we can say:
multiply 2nd equation by 2 getting 320=10b +10x    now add the first equation
160 = 10b -10x
320 = 10b +10x
---------------
480 = 20b
b=480/20 = 24mph (boat speed)
substitute 24 for b in any of the equations above
160= 5(24 + x)
160 = 120 +5x
5x =160 - 120
5x = 40
x =8 mph (current speed)

anonymous · Answer

Thank you for showing me ALL the steps Radar.

radar · Answer

You are welcome.