SOLUTION: A boat covers a certain distance downstream in 2 hours.it covers the same distance upstream in 2.5 hours. The speed of the boat i 18 km/hr. Find the speed of the water. Also fi

Algebra ->  Graphs -> SOLUTION: A boat covers a certain distance downstream in 2 hours.it covers the same distance upstream in 2.5 hours. The speed of the boat i 18 km/hr. Find the speed of the water. Also fi      Log On


   

Question 1039754: A boat covers a certain distance downstream in 2 hours.it covers the same distance upstream in 2.5 hours.
The speed of the boat i 18 km/hr.
Find the speed of the water. Also find the distance covered by the boat
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance boat covers going
either upstream or downstream in km
Let +c+ = the speed of the current in km/hr
-----------------------------------
Equation for going downstream:
(1) +d+=+%28+18+%2B+c+%29%2A2+
Equation for going upstream:
(2) +d+=+%28+18+-+c+%29%2A2.5+
--------------------------
(1) +d+=+36+%2B+2c+
(1) +d+-+2c+=+36+
and
(2) +d+=+45+-+2.5c+
(2) +d+%2B+2.5c+=+45+
----------------------
Subtract (1) from (2)
(2) +d+%2B+2.5c+=+45+
(1) +-d+%2B+2c+=+-36+
---------------------
+4.5c+=+9+
+c+=+2+ km/hr
and
(1) +d+=+%28+18+%2B+c+%29%2A2+
(1) +d+=+20%2A2+
(1) +d+=+40+ km
-------------------
The boat travels 40 km ( one way )
The speed of the current is 2 km/hr
---------------------------------
check:
(2) +d+=+%28+18+-+c+%29%2A2.5+
(2) +d+=+%28+18+-+2+%29%2A2.5+
(2) +d+=+16%2A2.5+
(2) +d+=+40+ km
OK