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

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) (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?
----
Upstream DATA:
time = 10 hrs ; distance = 15 miles ; rate = d/t = 15/10 = 1.5 mph
----------------
Downstream DATA:
time = 5 hrs ; distance = 22 miles ; rate = d/t = 22/5 = 4.4 mph
---------------
Equations:
upstream: b-c = 1.5 mph
downstream: b+c = 4.4 mph
-------------------------------
Add and solve for "b":
2b = 5.9 mph
b = 2.95 (speed of the boat in still water)
---
Solve for "c":
b + c = 4.4
2.95 + c = 4.4
c = 1.45 mph (speed of the current)
=============
Cheers,
Stan H.
=================
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = speed of boat in still water in mi/hr
Let = speed of current in mi/hr
= speed of boat going against the current in mi/hr
= speed of boat going with the current in mi/hr
-------------
given:
Going upstream:
(1)
(1)
Going downstream:
(2)
(2)
-----------------
(1)
(2)
add the equations:
(2)
(1)

and
(1)
(1)
(1)
(1)
The speed of the boat in still water is 3 mi/hr
The speed of the current is 1.5 mi/hr
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
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