SOLUTION: a tugboat goes 160 miles upstream in 20 hrs, the return trip downstream takes 5 hrs, what is the speed of the tug boat without the current and what is the speed of the current

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Question 638934: a tugboat goes 160 miles upstream in 20 hrs, the return trip downstream takes 5 hrs, what is the speed of the tug boat without the current and what is 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 boat without current
Let +c+ = the speed of the current
+s+-+c+ = speed going upstream
+s+%2B+c+ = speed going downstream
-----------------------------
Going upstream:
(1) +160+=+%28+s+-+c+%29%2A20+
Going downstream:
(2) +160+=+%28+s+%2B+c+%29%2A5+
-------------------
(1) +20s+-+20c+=+160+
(1) +s+-+c+=+8+
and
(2) +160+=+5s+%2B+5c+
(2) +s+%2B+c+=+32+
--------------
Add (1) and (2)
(1) +s+-+c+=+8+
(2) +s+%2B+c+=+32+
+2s+=+40+
+s+=+20+
and, since
(1) +s+-+c+=+8+
(1) +20+-+c+=+8+
(1) +-c+=+-12+
(1) +c+=+12+
The speed of the boat without current is 20 mi/hr
The speed of the current is 12 mi/hr
check:
(1) +160+=+%28+20+-+12+%29%2A20+
(1) +160+=+8%2A20+
(1) +160+=+160+
and
(2) +160+=+%28+20+%2B+12+%29%2A5+
(2) +160+=+32%2A5+
(2) +160+=+160+
OK