SOLUTION: A tugboat goes 180 miles upstream in 15hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without a current and the speed of the current

Algebra ->  Sequences-and-series -> SOLUTION: A tugboat goes 180 miles upstream in 15hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without a current and the speed of the current      Log On


   

Question 630585: A tugboat goes 180 miles upstream in 15hours. The return trip downstream takes 10 hours. 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 boat without a current
Let +c+ = the speed of the current
Going upstream:
(1) +180+=+%28+s+-+c+%29%2A15+
Going downstream:
(2) +180+=+%28+s+%2B+c+%29%2A10+
--------------------
(1) +180+=+15s+-+15c+
(1) +15s+=+180+%2B+15c+
(1) +s+=+12+%2B+c+
Substitute this into (2)
(2) +180+=+%28+12+%2B+c+%2B+c+%29%2A10+
(2) +180+=+120+%2B+20c+
(2) +20c+=+180+-+120+
(2) +20c+=+++60+
(2) +c+=+3+
and, since
(1) +180+=+%28+s+-+c+%29%2A15+
(1) +180+=+%28+s+-+3+%29%2A15+
(1) +180+=+15s+-+45+
(1) +15s+=+180+%2B+45+
(1) +15s+=+225+
(1) +s+=+15+
The speed of the boat without a current is 15 mi/hr
The speed of the current is 3 mi/hr
check answers:
(2) +180+=+%28+s+%2B+c+%29%2A10+
(2) +180+=+%28+15+%2B+3+%29%2A10+
(2) +180+=+18%2A10+
(2) +180+=+180+
OK