SOLUTION: A boat can travel 44 mph in still water. If it travels 147 miles with the current in the same length of time it travels 117 miles against the current, what is the speed of the curr

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Question 1154220: A boat can travel 44 mph in still water. If it travels 147 miles with the current in the same length of time it travels 117 miles against the current, what is the speed of the current?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current in mi/hr
Let +t+ = time for both trips in mi/hr
---------------------------------------------------
(1) +147+=+%28+44+%2B+c+%29%2At+
(2) +117+=+%28+44+-+c+%29%2At+
----------------------------------
Add the equations:
(1) +147+=+44t+%2B+c%2At++
(2) +117+=+44t+-+c%2At++
------------------------------
+264+=+88t+
+t+=+3+
---------------------
Plug this result back into (1) or (2)
(1) +147+=+%28+44+%2B+c+%29%2At+
(1) +147+=+%28+44+%2B+c+%29%2A3+
(1) +49+=+44+%2B+c+
(1) +c+=+5+
The current is 5 mi/hr
---------------------------
check:
(2) +117+=+%28+44+-+c+%29%2At+
(2) +117+=+%28+44+-+5+%29%2A3+
(2) +117+=+39%2A3+
(2) +117+=+117+
OK

Answer by MathTherapy(10810) About Me  (Show Source):
You can put this solution on YOUR website!

A boat can travel 44 mph in still water. If it travels 147 miles with the current in the same length of time it travels 117 miles against the current, what is the speed of the current?
Let speed of current be C

Then average speed downstream (with current) = 44 + C

Also, average speed upstream (against current) = 44 - C

We then get the following TIME equation: matrix%281%2C3%2C+147%2F%2844+%2B+C%29%2C+%22=%22%2C+117%2F%2844+-+C%29%29

matrix%281%2C3%2C+49%2F%2844+%2B+C%29%2C+%22=%22%2C+39%2F%2844+-+C%29%29 ------ Reducing fractions by factoring out GCF, 3, in numerator

39(44 + C) = 49(44 - C) ------ Cross-multiplying

39(44) + 39C = 49(44) - 49C

39C + 49C = 49(44) - 39(44)

88C = 10(44)

C, or 

It's as easy as A-B-C!