SOLUTION: Determine the speed of a motorboat in still water and the speed of the river current, if it takes 3 hrs to travel a distance of 45 miles upstream and 2 hrs to travel 50 miles downs

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Question 151378: Determine the speed of a motorboat in still water and the speed of the river current, if it takes 3 hrs to travel a distance of 45 miles upstream and 2 hrs to travel 50 miles downstream.
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Determine the speed of a motorboat in still water and the speed of the river current, if it takes 3 hrs to travel a distance of 45 miles upstream and 2 hrs to travel 50 miles downstream.
:
Let x = speed of boat in still water
Let y = speed of the current
then
(x+y) = speed with the current
and
(x-y) = speed against the current
:
Write a distance equation for each trip: Dist = time * speed
;
2(x + y) = 50
3(x - y) = 45
;
Simplify divide the 1st equation by 2 and the 2nd equation by 3; results:
x + y = 25
x - y = 15
------------addition eliminates y, find x
2x = 40
x =
x = 20 mph speed of boat in still water
:
Find y using; x + y = 25
20 + y = 25
y = 25 - 20
y = 5 mph speed of the river
:
:
Check solutions in the 2nd original equation
3(x - y) = 45
3(20-5) = 45
3(15) = 45; confirms our solution

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Determine the speed of a motorboat in still water and the speed of the river current, if it takes 3 hrs to travel a distance of 45 miles upstream and 2 hrs to travel 50 miles downstream.
----------------------------
Let speed of boat be "b".
Let speed of current be "c".
-------------
Upstream DATA:
distance = 45 miles ; time = 3 hrs; rate = 45/3 = 15 mph
---------------
Downstream DATA:
distance = 50 miles ; time = 2 hrs; rate = 50/2 = 25 mph
===============
EQUATIONS:
b + c = 25 mph
b - c = 15 mph
------------------
Add to get:
2b = 40
b = 20 mph (boat speed in still water)
-------------
Since b + c = 25, c = = 25-20 = 5 mph (current speed)
-------------------------
Cheers,
Stan H.