SOLUTION: it takes bob the boy scout 10 hours to paddle upstream against the current a distance of 15 miles. when he turn around he finds it only takes him 5 hours to 'paddle 22.5 miles with

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: it takes bob the boy scout 10 hours to paddle upstream against the current a distance of 15 miles. when he turn around he finds it only takes him 5 hours to 'paddle 22.5 miles with      Log On


   

Question 571547: it takes bob the boy scout 10 hours to paddle upstream against the current a distance of 15 miles. when he turn around he finds it only takes him 5 hours to 'paddle 22.5 miles with current. how fast is bob's boat going in still water and what is the speed of the current of the river?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
it takes bob the boy scout 10 hours to paddle upstream against the current a distance of 15 miles. when he turn around he finds it only takes him 5 hours to 'paddle 22.5 miles with current. how fast is bob's boat going in still water and what is the speed of the current of the river?
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Upstream DATA:
time = 10 hrs ; distance = 15 miles ; rate = d/t = 15/10 = 1.5 mph
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Downstream DATA:
time = 5 hrs ; distance = 22 miles ; rate = d/t = 22/5 = 4.4 mph
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Equations:
upstream: b-c = 1.5 mph
downstream: b+c = 4.4 mph
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Add and solve for "b":
2b = 5.9 mph
b = 2.95 (speed of the boat in still water)
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Solve for "c":
b + c = 4.4
2.95 + c = 4.4
c = 1.45 mph (speed of the current)
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = speed of boat in still water in mi/hr
Let +c+ = speed of current in mi/hr
+s+-+c+ = speed of boat going against the current in mi/hr
+s+%2B+c+ = speed of boat going with the current in mi/hr
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given:
Going upstream:
(1) +d%5B1%5D+=+%28+s+-+c+%29%2At%5B1%5D+
(1)+15+=+%28+s+-+c+%29%2A10+
Going downstream:
(2) +d%5B2%5D+=+%28+s+%2B+c+%29%2At%5B2%5D+
(2) +22.5+=+%28+s+%2B+c+%29%2A5+
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(1) +s++-+c+=+3%2F2+
(2) +s+%2B+c+=++4.5+
add the equations:
(2) +s+%2B+c+=++4.5+
(1) +s+-+c+=+3%2F2+
+2s+=+6+
+s+=+3+
and
(1) +s++-+c+=+3%2F2+
(1) +3++-+c+=+3%2F2+
(1) +-c+=+-1.5+
(1) +c+=+1.5+
The speed of the boat in still water is 3 mi/hr
The speed of the current is 1.5 mi/hr
check:
(1)+15+=+%28+s+-+c+%29%2A10+
(1) +15+=+%28+3+-+1.5+%29%2A10+
(1) +15+=+1.5%2A10+
(1) +15+=+15+
and
(2) +22.5+=+%28+s+%2B+c+%29%2A5+
(2) +22.5+=+%28+3+%2B+1.5+%29%2A5+
(2) +22.5+=+4.5%2A5+
(2) +22.5+=+22.5+
OK