SOLUTION: please help me with this problem. a motorboat with the current went 54mi in 3 hours. against the current, it took 3.6 hours to travel the same distance. find the rate of the boat i

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Question 692018: please help me with this problem. a motorboat with the current went 54mi in 3 hours. against the current, it took 3.6 hours to travel the same distance. find the rate of the boat in calm water and the rate of the current.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
b = rate of the boat in calm water (in miles per hour)
c = rate of the current (in miles per hour)

With the current, the boat moves at b%2Bc miles per hour.
In 3 hours it covers a distance (in miles) of
3%28b%2Bc%29=54

Against the current, the boat moves at b-c miles per hour.
In 3.6 hours it covers a distance (in miles) of
3.6%28b-c%29=54

Those two equations form a system of linear equations that needs to be solved for b and c,
but they can be simplified a bit.
3%28b%2Bc%29=54 --> 3%28b%2Bc%29%2F3=54%2F3 --> b%2Bc=18
3.6%28b-c%29=54 --> 3.6%28b-c%29%2F3.6=54%2F3.6 --> b-c=15
Now we can write the system as
system%28b%2Bc=18%2Cb-c=15%29

You can easily solve the system by substitution, or by elimination.

BY ELIMINATION:
Adding both equations, we get
2b=18%2B15 --> 2b=33 --> 2b%2F2=33%2F2 --> highlight%28b=16.5%29
Substituting that into b%2Bc=18%7D%7D%2C+we+get%0D%0A%7B%7B%7B16.5%2Bc=18 --> 16.5%2Bc-16.5=18-16.5 --> highlight%28c=1.5%29

BY SUBSTITUTION:
b-c=15 --> b-c%2Bc=15%2Bc --> b=15%2Bc
Substituting 15%2Bc for b in b%2Bc=18, we get
15%2Bc%2Bc=18 --> 15%2B2c=18 --> 15%2B2c-18=18-15 --> 2c=3 --> 2c%2F2=3%2F2 --> highlight%28c=1.5%29
Substituting that into b=15%2Bc, we get
b=15%2B1.5 --> highlight%28b=16.5%29