SOLUTION: A boat can travel 114 miles downstream in the same time that it can travel 24 miles upstream. If the boat can travel 23 miles per hour in still water,find the speed of the current.

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Question 515181: A boat can travel 114 miles downstream in the same time that it can travel 24 miles upstream. If the boat can travel 23 miles per hour in still water,find the speed of the current.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = speed of current
Let s = speed of boat in still water
given:
Going downstream:
(1) +114+=+%28+s+%2B+c+%29%2At+
Going upstream:
(2) +24+=+%28+s+-+c+%29%2At+
-------------------
(1) +114+=+%28+23+%2B+c+%29%2At+
(2) +24+=+%28+23+-+c+%29%2At+
-------------------
(1) +114+=+23t+%2B+c%2At+
(2) +24+=+23t+-+c%2At+
Add the equations
+138+=+46t+
+t+=+3+
and, since
(1) +114+=+23t+%2B+c%2At+
(1) +114+=+23%2A3+%2B+3c+
(1) +3c+=+114+-+69+
(1) +3c+=+45+
(1) +c+=+15+
The speed of the current is 15 mi/hr
check:
(2) +24+=+%28+s+-+c+%29%2At+
(2) +24+=+%28+23+-+15+%29%2A3+
(2) +24+=+8%2A3+
(2) +24+=+24+
OK