SOLUTION: A boat that goes 12 miles per hour in still water takes as long to go 16 miles upstream as to go 32 miles downstream. Find the velocity of the stream. can you please give an equ

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Question 938311: A boat that goes 12 miles per hour in still water takes as long to go 16 miles upstream as to go 32 miles downstream. Find the velocity of the stream.
can you please give an equation and detailed explanation
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
RT=D rate time distance, uniform rates for travel basic rule.

Let c be speed of stream or current
Given 12 mph speed of goat if current in stream absent
Let t be time either direction


__________________speed_________time_________distance
Upstream__________12-c__________t____________16
Downstrm__________12+c__________t____________32

System of equations

Solve the system, a few (or more) algebra steps.

A good way to go is,
solve one equation for t, and substitute this into the other equation; and then solve this for c. You might be first tempted to "simplify" the equations of the system but that might make more steps and more work.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
A boat that goes 12 miles per hour in still water takes as long to go 16 miles upstream as to go 32 miles downstream. Find the velocity of the stream.
can you please give an equation and detailed explanation
Let stream’s speed, be S

Then we get: 

   32(12 – S) = 16(12 + S) ----- Cross-multiplying

   384 – 32S = 192 + 16S 

– 32S – 16S = 192 – 384 

          – 48S = – 192

S, or stream’s speed = , or  mph      

You can do the check!! 

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