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

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Question 470473: 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 formula. Thanks!
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let represent the distance for either of the trips which we know to be 60 miles. Let represent the rate of the boat in still water. Let represent the rate of the current. Let represent the time for the downstream trip which we know to be 2 hours. And let represent the time for the upstream trip which we know to be 6 hours.

When the boat is going downstream, the rate of the boat relative to the stationary bank of the river is the rate of the boat in still water PLUS the rate of the current. Conversely, going upstream the rate of the boat relative to the bank is the rate in still water MINUS the rate of the current.

We can describe the downstream trip thus:



and the upstream trip:



Now plug in the known values:





A little manipulation:





Solve the first equation for in terms of



Substitute the RHS expression in place of in the second equation.



All that is left is to solve for

John

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