SOLUTION: a boat heads upstream a distance of 30 miles on the missisippi river,whose current is running at 5 mph. if the trip back takes an hour less, what was the speed of the boat in still

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Question 342305: a boat heads upstream a distance of 30 miles on the missisippi river,whose current is running at 5 mph. if the trip back takes an hour less, what was the speed of the boat in still water? answer rounded to 2 decimal places if needed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need 2 equations: 1 for upstream and 1 for downstream
d%5Bu%5D+=+r%5Bu%5D%2A+t%5Bu%5D
d%5Bd%5D+=+r%5Bd%5D%2A+t%5Bd%5D
Let rate of current = r%5Bc%5D
Let rate in still water = r%5Bs%5D
r%5Bu%5D+=+r%5Bs%5D+-+r%5Bc%5D mi/hr
r%5Bd%5D+=+r%5Bs%5D+%2B+r%5Bc%5D mi/hr
given:
d%5Bu%5D+=+30 mi
d%5Bd%5D%5D+=+30 mi
r%5Bc%5D+=+5 mi/hr
t%5Bd%5D+=+t%5Bu%5D+-+1 hr
r%5Bu%5D+=+r%5Bs%5D+-+5 mi/hr
r%5Bd%5D+=+r%5Bs%5D+%2B+5 mi/hr
-----------------
d%5Bu%5D+=+r%5Bu%5D%2A+t%5Bu%5D
30+=+%28r%5Bs%5D+-+5%29%2At%5Bu%5D
t%5Bu%5D+=+30%2F%28r%5Bs%5D+-+5%29
and
d%5Bd%5D+=+r%5Bd%5D%2A+t%5Bd%5D
30+=+%28r%5Bs%5D+%2B+5%29%2A+%28t%5Bu%5D+-+1%29
30+=+r%5Bs%5D%2At%5Bu%5D+%2B+5t%5Bu%5D+-+r%5Bs%5D+-+5
By substitution:

Multiply both sides by r%5Bs%5D+-+5
30%2A%28r%5Bs%5D+-+5%29+=+30r%5Bs%5D+%2B+150+-+%28r%5Bs%5D+%2B+5%29%2A%28r%5Bs%5D+-+5%29
30r%5Bs%5D+-+150+=+30r%5Bs%5D+%2B+150+-+%28r%5Bs%5D%29%5E2+-+25
%28r%5Bs%5D%29%5E2++=+275
r%5Bs%5D+=+16.58 mi/hr
check answer:
30+=+%28r%5Bs%5D+-+5%29%2At%5Bu%5D
30+=+%2816.58+-+5%29%2At%5Bu%5D
30+=+11.58%2At%5Bu%5D
t%5Bu%5D+=+2.59 hrs
t%5Bd%5D+=+1.59 hrs
r%5Bu%5D+=+r%5Bs%5D+-+5
r%5Bu%5D+=+16.58+-+5
r%5Bu%5D+=+11.58
r%5Bd%5D+=+16.58+%2B+5
r%5Bd%5D+=+21.58
d%5Bd%5D+=+r%5Bd%5D%2A+t%5Bd%5D
30+=+21.58%2A1.59
30+=+34.31 this is wrong
d%5Bu%5D+=+r%5Bu%5D%2A+t%5Bu%5D
30+=+11.58%2A2.59
30+=+29.99 OK
Something went wrong somewhere- answer doesn't
quite check. My method is good, though.
See if you can find error