SOLUTION: Time taken by a boat in covering a distance upstream is 1.5times to that of covering the same distance downstream.What will be the ratio between speed of the boat in still water an

Algebra ->  Finance -> SOLUTION: Time taken by a boat in covering a distance upstream is 1.5times to that of covering the same distance downstream.What will be the ratio between speed of the boat in still water an      Log On


   

Question 1110187: Time taken by a boat in covering a distance upstream is 1.5times to that of covering the same distance downstream.What will be the ratio between speed of the boat in still water and that of stream
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs to travel downstream
+1.5t+ = time in hrs to travel upstream
Let +d+ = one way distance
Let +s+ = the speed of the boat in still water
Let +c+ = the speed of the current
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Equation for going upstream:
(1) +d+=+%28+s+-+c+%29%2A1.5t+
Equation for going downstream:
(2) +d+=+%28+s+%2B+c+%29%2At+
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+%28+s+-+c+%29%2A1.5t+=+%28+s+%2B+c+%29%2At+
+1.5%2A%28+s+-+c+%29+=+s+%2B+c+
+1.5s+-+1.5c+=+s+%2B+c+
+.5s+=+2.5c+
+s%2Fc+=+2.5%2F.5+
+s%2Fc+=+5%2F1+

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


For the same distance, the ratio of times is 1.5:1, or 3:2; that means the ratio of speeds is 2:3.

If b is the boat's speed and c is the speed of the current, then the upstream speed is b-c and the downstream speed is b+c. So

%28b-c%29%2F%28b%2Bc%29+=+2%2F3
3%28b-c%29+=+2%28b%2Bc%29
3b-3c+=+2b%2B2c
b+=+5c
b%2Fc+=+5

The ratio of the boat's speed to the speed of the current is 5:1.