SOLUTION: A tugboat goes 160 miles an hour upstream in 20 hrs. The return trip downstream takes 10 hrs. Find the speed of the tugboat without a current and the speed of the current.

Algebra ->  Test -> SOLUTION: A tugboat goes 160 miles an hour upstream in 20 hrs. The return trip downstream takes 10 hrs. Find the speed of the tugboat without a current and the speed of the current.      Log On


   

Question 621016: A tugboat goes 160 miles an hour upstream in 20 hrs. The return trip downstream takes 10 hrs. Find the speed of the tugboat without a current and the speed of the current.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the tugboat without a current
Let +c+ = the speed of the current
Going upstream:
(1) +160+=+%28+s+-+c+%29%2A20+
-------------
Going downstream:
(2) +160+=+%28+s+%2B+c+%29%2A10+
--------------------
(1) +s+-+c+=+8+
and
(2) +s+%2B+c+=+16+
---------------
Add (1) and (2)
(1) +s+-+c+=+8+
(2) +s+%2B+c+=+16+
+2s+=+24+
+s+=+12+
and, since
(1) +s+-+c+=+8+
(1) +12+-+c+=+8+
(1) +-c+=-4+
(1) +c+=+4+
The speed of the tugboat without a current is 12 mi/hr
The speed of the current is 4 mi/hr
check:
(1) +160+=+%28+s+-+c+%29%2A20+
(1) +160+=+%28+12+-+4+%29%2A20+
(1) +160+=+8%2A20+
(1) +160+=+160+
OK