SOLUTION: A boat takes 6 hrs to travel 8 km upstream and 32 km downstreams and it takes 7 hrs to travel 20 km upstream and 16 km downztream. Find the speed of boat in still water and speed o

Algebra ->  Finance -> SOLUTION: A boat takes 6 hrs to travel 8 km upstream and 32 km downstreams and it takes 7 hrs to travel 20 km upstream and 16 km downztream. Find the speed of boat in still water and speed o      Log On


   

Question 1062938: A boat takes 6 hrs to travel 8 km upstream and 32 km downstreams and it takes 7 hrs to travel 20 km upstream and 16 km downztream. Find the speed of boat in still water and speed of stream
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s = the speed of the boat in still water in km/hr
Let +c+ = the speed of the current in km/hr
---------------------------------------------------
Equation for traveling upsteam
(1) +8+=+%28+s+-+c+%29%2A6+
Equation for traveling downstream:
(2) +32+=+%28+s+%2B+c+%29%2A6+
------------------------------------
(1) +8+=+6s+-+6c+
(1) +3s+-+3c+=+4+
and
(2) +32+=+6s+%2B+6c+
(2) +3s+%2B+3c+=+16+
-------------------------
add (1) and (2)
(1) +3s+-+3c+=+4+
(2) +3s+%2B+3c+=+16+
--------------------------
+6s+=+20+
+s+=+10%2F3+ km/hr
and
(1) +3s+-+3c+=+4+
(1) +3%2A%2810%2F3%29+-+3c+=+4+
(1) +10+-+3c+=+4+
(1) +3c+=+6+
(1) +c+=+2+ km/hr
-----------------------
check answer
(1) +8+=+%28+s+-+c+%29%2A6+
(1) +8+=+%28+10%2F3+-+6%2F3+%29%2A6+
(1) +8+=+%284%2F3%29%2A6+
(1) +8+=+8+
and
(2) +32+=+%28+s+%2B+c+%29%2A6+
(2) +32+=+%28+10%2F3+%2B+6%2F3+%29%2A6+
(2) +32+=+%2816%2F3%29%2A6+
(2) +32+=+32+
OK
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Is the 2nd part a different boat? Anyway, you
solve it the same way I just did. check the math.