SOLUTION: 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 i

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!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance
that's the basic equation used to solve these type of problems.
the other fact to consider is:
going with the stream, the rate of the boat and the rate of the stream are additive.
going against the stream, the rate of the boat and the rate of the stream are subtractive.
you are given:
cruise boat travels 60 miles downstream in 2 hours.
cruise boat travels 60 miles upstream in 6 hours.
you are asked to find the speed of the stream.
you have the speed of the boat and the speed of the stream.
let b be the speed of the boat and let s be the speed of the stream.
going downstream, the equation is:
(b + s) * 2 = 60
(b + s) is the rate
2 hours is the time
60 milesis the distance.
going upstream, the equation is:
(b - s) * 6 = 60
those are your 2 equations.
solve them simultaneously and you will be able to get the answer to the problem.
the 2 equations are:
(b + s) * 2 = 60
(b - s) * 6 = 60
expand the left side of the equation to get:
2b + 2s = 60
6b - 6s = 60
we'll use the elimination method.
multiply the first equation by 3 to get:
6b + 6s = 180 (first equation multiplied by 3)
6b - 6s = 60 (second equation left as is)
add the second and first equation together to get:
12b = 240
divide both sides of this equation by 12 to get:
b = 20
use the value of b to solve for s in either of the 2 original equations.
we'll choose 2b + 2s = 60
substitute 20 for b to get:
40 + 2s = 60
subtract 40 from both sides of the equation to get:
2s = 20
divide both sides of the equation by 2 to get:
s = 10
our solutions appear to be:
b = 20
s = 10
going downstream, our equation was:
(b + s) * 2 = 60
this becomes:
(20 + 10) * 2 = 60 which becomes 30 * 2 = 60 which becomes 60 = 60.
going upstream, our equation was:
(b - s) * 6 = 60
this becomes:
(20 - 10) * 6 = 60 which becomes 10 * 6 = 60 which becomes 60 = 60.
our values for b and s are good.
the speed of the boat is 20 miles per hour.
the speed of the stream is 10 miles per hour.

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