SOLUTION: A boat travels slong a river with a current of 2 miles per hour. If the boat travels 30 miles up river and then returns the same distance in a total time of eight hours, what is th

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Question 268976: A boat travels slong a river with a current of 2 miles per hour. If the boat travels 30 miles up river and then returns the same distance in a total time of eight hours, what is the boat's speed in still water?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is an RTD problem. Here is a table based on the given information
boats . . . . . . . .rate . . . . . . . . .time . . . . . . . . . distance
up . . . . . . . . . .r - 2 . . . . . . . . 30/(r-2). . . . . . . . . 30
down . . . . . . . r + 2. . . . . . . . .30/(r+2). . . . . . . . . 30 . .
totals . . . . . . . . . . . . . . . . . . . .8. . . . . . . . . . . . . . . . .
total time equal to the sum of upstream and downstream time. We get
(i) 30%2F%28r%2B2%29+%2B+30%2F%28r-2%29+=+8
step 1 - multiply by (r+2)(r-2) as the common denominator, we get
(ii) 30%28r-2%29+%2B+30%28r%2B2%29+=+8r%5E2-32
step 2 - simplify the left to get
(iii) 60r+=+8r%5E2+-+32
step 3 - set = 0 as
(iv) 8r%5E2+-+60r+-+32+=+0
step 4 - divide by 4 to get
(v) 2r%5E2+-+15r+-+8+=+0
step 5 - factor to get
(vi) %28r-8%29%28r%2B1%29+=+0
So, we get
r = 8.