SOLUTION: hello there i have a word problem which i have been working on for the past couple of minutes and im quite stuck the problem reads as following: a boat can travel 8mph in s

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Question 686684: hello there i have a word problem which i have been working on for the past couple of minutes and im quite stuck the problem reads as following:
a boat can travel 8mph in still water and travel 36 miles upstream in twice the time it can travel 30 miles downstream find the rate of the current.
my problem is with the 36 in twice the time it can travel 30 miles downstream, i dont know how to write that down.
i have te rate of the boat as (8+r) for the downstream and 8-r for downstream
please help, thanks
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You rightly concluded that the boat goes upstream at %288-r%29 mph
and downstream at %288%2Br%29 mph.
The time needed to travel 30 miles downstream is 30%2F%288%2Br%29
The time to travel 36 miles upstream is 36%2F%288-r%29,
which is twice as long a time, so
highlight%2836%2F%288-r%29=2%2A%2830%2F%288%2Br%29%29%29
Now that we have our equation, we solve it
36%2F%288-r%29=2%2A%2830%2F%288%2Br%29%29 --> 36%2F%288-r%29=60%2F%288%2Br%29 to simplify it a bit.
Form there, we "equate the cross-products",
which is the same as multiplying both sides times %288-r%29%288%2Br%29
36%2F%288-r%29=60%2F%288%2Br%29 --> 36%288%2Br%29=60%288-r%29 --> 36%2A8%2B36r=60%2A8-60r --> 288%2B36r=480-60r
288%2B36r=480-60r --> 288%2B36r%2B60r-288=480-60r%2B60r-288 --> 36r%2B60r=480-288 --> 96r=192 --> 96r%2F96=192%2F96 --> highlight%28r=2%29