SOLUTION: The speed of a stream is 6 mph. If a boat travels 72 miles downstream in the same time that it takes to travel 36 miles upstream, what is the speed of the boat in still water?

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Question 42785: The speed of a stream is 6 mph. If a boat travels 72 miles downstream in the same time that it takes to travel 36 miles upstream, what is the speed of the boat in still water?
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
We could consider the speed of the boat as x and the stream as y. The stream takes the boat forward or backwards, so we have two equations: x + y = 72 (the downstream takes the boat forward) and x - y = 36.
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+72%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+36+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
1%2Ax+=+72+-+1%2Ay, or x+=+72%2F1+-+1%2Ay%2F1. Substitute that
into another equation:
1%2A%2872%2F1+-+1%2Ay%2F1%29+%2B+-1%5Cy+=+36 and simplify: So, we know that y=18. Since x+=+72%2F1+-+1%2Ay%2F1, x=54.

Answer: system%28+x=54%2C+y=18+%29.

If y=18, the "time" we took is y/6 = 3 hours, and x is the speed of the boat in three hours. The answer we want is better given in an hour period, so our answer is 54%2F3+=+18 mph.