document.write( "Question 201570: A ship went up a stream of 36km in 3 hours, and went down the same distance in 2 hours. What is the km per hour for this ship if there is no speed in this stream? What is this stream's km per hour?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #151802 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the ship is travelling at 15 kilometers per hour.
\n" ); document.write( "the stream is travelling at 3 kilometers per hour.
\n" ); document.write( "here's how to figure it out.
\n" ); document.write( "let x = speed of ship.
\n" ); document.write( "let y = speed of water.
\n" ); document.write( "rate and speed mean the same thing, at least here.
\n" ); document.write( "general formula is rate times time = distance.
\n" ); document.write( "you can also say speed times time = distance.
\n" ); document.write( "ship and boat mean the same thing here also.
\n" ); document.write( "going with the current of the water, the rate of speed of the water adds to the rate of speed of the boat.
\n" ); document.write( "going against the current of the water, the rate of speed of the water detracts (subtracts) from the speed of the boat.
\n" ); document.write( "so, going with the current of the water, the rate of the boat and the water is x + y, and going against the current of the water, the rate of the boat and the water is x - y.
\n" ); document.write( "since rate times time = distance, we have:
\n" ); document.write( "3 (x-y) = 36 which is going against the current of the water.
\n" ); document.write( "and we have
\n" ); document.write( "2 (x + y) = 36 which is going with the current of the water.
\n" ); document.write( "since they both equal 36, then they are equal to each other so we have
\n" ); document.write( "3 * (x-y) = 2 * (x + y)
\n" ); document.write( "removing parentheses, we get
\n" ); document.write( "3x - 3y = 2x + 2y
\n" ); document.write( "subtracting 2x from both sides and adding 3 y to both sides, we get
\n" ); document.write( "x = 5y
\n" ); document.write( "this means that the rate of the boat is 5 times the rate of the water.
\n" ); document.write( "now that we know one of the unknowns, we can solve for the other.
\n" ); document.write( "take either equation and solve for y.
\n" ); document.write( "using 2 * (x + y) = 36, and replacing x with 5y, we get
\n" ); document.write( "2 * (5y + y) = 36
\n" ); document.write( "which becomes
\n" ); document.write( "2 * 6y = 36
\n" ); document.write( "which becomes
\n" ); document.write( "12 * y = 36
\n" ); document.write( "which becomes
\n" ); document.write( "y = 3
\n" ); document.write( "so, the rate of the water is 3 km per hour.
\n" ); document.write( "since the boat is 5 times this, then the rate of the boat is 15 kmph.
\n" ); document.write( "making x = 15 and y = 3, and substituting in the other equation, we get
\n" ); document.write( "3 * ( x-y) = 36
\n" ); document.write( "becomes
\n" ); document.write( "3 * (15-3) = 36
\n" ); document.write( "becomes
\n" ); document.write( "3 * (12) = 36
\n" ); document.write( "becomes
\n" ); document.write( "36 = 36
\n" ); document.write( "answer is true so the values are good.
\n" ); document.write( "answer is:
\n" ); document.write( "rate of the ship is 15 kmph
\n" ); document.write( "rate of the water is 3 kmph
\n" ); document.write( " \n" ); document.write( "
\n" );