SOLUTION: A tug tows a bard 24 miles up a river at 10mph and returns down the river at 12 mph. The entire trip takes 5.5 hours. What is the rate of the river's current? Since this problem

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A tug tows a bard 24 miles up a river at 10mph and returns down the river at 12 mph. The entire trip takes 5.5 hours. What is the rate of the river's current? Since this problem      Log On

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Question 214879: A tug tows a bard 24 miles up a river at 10mph and returns down the river at 12 mph. The entire trip takes 5.5 hours. What is the rate of the river's current?
Since this problem doesn't provide the elapsed time of each trip, I am having trouble setting it up.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll write 2 equations, 1 for upriver
and 1 for downriver.
d%5Bu%5D+=+r%5Bu%5D%2At%5Bu%5D
and
d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D
Let the rate of the river's current = r%5Bc%5D
Let r%5Bb%5D = the rate of the boat in still water
given:
d%5Bu%5D+=+24 mi
d%5Bd%5D+=+24 mi
r%5Bu%5D+=+10 mi/hr
r%5Bd%5D+=+12 mi/hr
t%5Bu%5D+%2B+t%5Bd%5D+=+5.5 hr
--------------------------
d%5Bu%5D+=+r%5Bu%5D%2At%5Bu%5D
24+=+10%2At%5Bu%5D
and
24+=+12%2At%5Bd%5D
From these,
t%5Bu%5D+=+2.4
t%5Bd%5D+=+2
Let r%5Bu%5D+=+r%5Bb%5D+-+r%5Bc%5D
Let r%5Bd%5D+=+r%5Bb%5D+%2B+r%5Bc%5D
and
r%5Bb%5D+=+r%5Bu%5D+%2B+r%5Bc%5D
r%5Bb%5D+=+r%5Bd%5D+-+r%5Bc%5D
r%5Bb%5D+=+10+%2B+r%5Bc%5D
r%5Bb%5D+=+12+-+r%5Bc%5D
So,
10+%2B+r%5Bc%5D+=+12+-+r%5Bc%5D
2r%5Bc%5D+=+2
r%5Bc%5D+=+1 mi/hr
The rate of the current is 1 mi/hr
check answer:
d%5Bu%5D+=+r%5Bu%5D%2At%5Bu%5D
d%5Bu%5D+=+%28r%5Bb%5D+-+r%5Bc%5D%29%2At%5Bu%5D
24+=+%28r%5Bb%5D+-+1%29%2A2.4
24+=+2.4r%5Bb%5D+-+2.4
2.4r%5Bb%5D+=+26.4
r%5Bb%5D+=+11 mi/hr
and
d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D
d%5Bd%5D+=+%28r%5Bb%5D+%2B+r%5Bc%5D%29%2At%5Bd%5D
24+=+%28r%5Bb%5D+%2B+1%29%2A2
24+=+2r%5Bb%5D+%2B+2
2r%5Bb%5D+=+22
r%5Bb%5D+=+11 mi/hr
OK