SOLUTION: A riverboat that sails at a rate of 18 miles per hour in still water can go 63 miles down the river in the same time it takes it to go 45 miles up the river. What is the speed of t

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A riverboat that sails at a rate of 18 miles per hour in still water can go 63 miles down the river in the same time it takes it to go 45 miles up the river. What is the speed of t      Log On

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Question 599470: A riverboat that sails at a rate of 18 miles per hour in still water can go 63 miles down the river in the same time it takes it to go 45 miles up the river. What is the speed of the current of the river?
Okay, so what i'm confused on is like how to set it up. We were taught the box method so with rate, distance, and time. I'm getting a giant decimal number when i put my numbers in... Can anyone help me? Thanks for your help in advance!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed in mi/hr of the current
Let +s+ = the speed in mi/hr of the boat in still water
Let +d+ = distance traveled in mi
Let +t+ = time in hours
----------------------
Going downriver:
+d+=+%28+s+%2B+c+%29%2At+
(1) +63+=+%28+18+%2B+c+%29%2At+
------------------
Going upriver:
+d+=+%28+s+-+c%29%2At+
(2) +45+=+%28+18+-+c+%29%2At+
------------------
(1) +t+=+63%2F%28+18+%2B+c+%29+
(2) +t+=+45%2F%28+18+-+c+%29+
---------------------
+63%2F%28+18+%2B+c+%29+=+45%2F%28+18+-+c+%29+
+63%2A%28+18+-+c+%29+=+45%2A%28+18+%2B+c+%29+
+1134+-+63c+=+810+%2B+45c+
+108c+=+324+
+c+=+3+
The speed of the current is 3 mi/hr
check:
(1) +t+=+63%2F%28+18+%2B+3+%29+
(2) +t+=+45%2F%28+18+-+3+%29+
--------------------
(1) +t+=+63%2F21+
(1) +t+=+3+ hrs
(2) +t+=+45%2F15+
(2) +t+=+3+ hrs
OK