document.write( "Question 470471: This is a story problem. I must have 2 equations so I can do the substitution method to solve. The problem is: A cruise boat travels 60 miles downstream in 2 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream. If you could show me how to solve this using the 2 equations and the d=r.t Thanks! \n" ); document.write( "
Algebra.Com's Answer #322685 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
rate * time = distance
\n" ); document.write( "that's the basic equation used to solve these type of problems.
\n" ); document.write( "the other fact to consider is:
\n" ); document.write( "going with the stream, the rate of the boat and the rate of the stream are additive.
\n" ); document.write( "going against the stream, the rate of the boat and the rate of the stream are subtractive.
\n" ); document.write( "you are given:
\n" ); document.write( "cruise boat travels 60 miles downstream in 2 hours.
\n" ); document.write( "cruise boat travels 60 miles upstream in 6 hours.
\n" ); document.write( "you are asked to find the speed of the stream.
\n" ); document.write( "you have the speed of the boat and the speed of the stream.
\n" ); document.write( "let b be the speed of the boat and let s be the speed of the stream.
\n" ); document.write( "going downstream, the equation is:
\n" ); document.write( "(b + s) * 2 = 60
\n" ); document.write( "(b + s) is the rate
\n" ); document.write( "2 hours is the time
\n" ); document.write( "60 milesis the distance.
\n" ); document.write( "going upstream, the equation is:
\n" ); document.write( "(b - s) * 6 = 60
\n" ); document.write( "those are your 2 equations.
\n" ); document.write( "solve them simultaneously and you will be able to get the answer to the problem.
\n" ); document.write( "the 2 equations are:
\n" ); document.write( "(b + s) * 2 = 60
\n" ); document.write( "(b - s) * 6 = 60
\n" ); document.write( "expand the left side of the equation to get:
\n" ); document.write( "2b + 2s = 60
\n" ); document.write( "6b - 6s = 60
\n" ); document.write( "we'll use the elimination method.
\n" ); document.write( "multiply the first equation by 3 to get:
\n" ); document.write( "6b + 6s = 180 (first equation multiplied by 3)
\n" ); document.write( "6b - 6s = 60 (second equation left as is)
\n" ); document.write( "add the second and first equation together to get:
\n" ); document.write( "12b = 240
\n" ); document.write( "divide both sides of this equation by 12 to get:
\n" ); document.write( "b = 20
\n" ); document.write( "use the value of b to solve for s in either of the 2 original equations.
\n" ); document.write( "we'll choose 2b + 2s = 60
\n" ); document.write( "substitute 20 for b to get:
\n" ); document.write( "40 + 2s = 60
\n" ); document.write( "subtract 40 from both sides of the equation to get:
\n" ); document.write( "2s = 20
\n" ); document.write( "divide both sides of the equation by 2 to get:
\n" ); document.write( "s = 10
\n" ); document.write( "our solutions appear to be:
\n" ); document.write( "b = 20
\n" ); document.write( "s = 10
\n" ); document.write( "going downstream, our equation was:
\n" ); document.write( "(b + s) * 2 = 60
\n" ); document.write( "this becomes:
\n" ); document.write( "(20 + 10) * 2 = 60 which becomes 30 * 2 = 60 which becomes 60 = 60.
\n" ); document.write( "going upstream, our equation was:
\n" ); document.write( "(b - s) * 6 = 60
\n" ); document.write( "this becomes:
\n" ); document.write( "(20 - 10) * 6 = 60 which becomes 10 * 6 = 60 which becomes 60 = 60.
\n" ); document.write( "our values for b and s are good.
\n" ); document.write( "the speed of the boat is 20 miles per hour.
\n" ); document.write( "the speed of the stream is 10 miles per hour.
\n" ); document.write( " \n" ); document.write( "
\n" );