SOLUTION: It took a patrol boat 5 hours to travel 60km up a river against the current, and 3 hours for the return trip with the current. Find the speed of the boat in still water and the spe

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: It took a patrol boat 5 hours to travel 60km up a river against the current, and 3 hours for the return trip with the current. Find the speed of the boat in still water and the spe      Log On


   

Question 215095: It took a patrol boat 5 hours to travel 60km up a river against the current, and 3 hours for the return trip with the current. Find the speed of the boat in still water and the speed of the current.
Can you please solve this, i cant seem to figure the answer when they mention still water. please can you show me how you do it please!
please and thank you
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It took a patrol boat 5 hours to travel 60km up a river against the current,
and 3 hours for the return trip with the current.
Find the speed of the boat in still water and the speed of the current
:
Let s = boat speed in still water
Let c = speed of the current
then
(s+c) = speed down river (with the current)
and
(s-c) = speed up river (against the current)
:
Write two distance equations, Dist = time * speed
3(s + c) = 60; down river
5(s - c) = 60; up-river
;
We can simplify both these equations
Divide the 1st by 3 and the 2nd equation by 5, results
s + c = 20
s - c = 12
-------------addition eliminates c find s
2s = 32
s = 32%2F2
s = 16 mph is the speed in still water
:
Find c using eq: s + c = 20
16 + c = 20
c = 20 - 16
c = 4 mph is the speed of the current
:
:
Check solution in the 2nd original equation
5(16 - 4) =
5(12) = 60 mi

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
It took a patrol boat 5 hours to travel 60km up a river against the current, and 3 hours for the return trip with the current. Find the speed of the boat in still water and the speed of the current.
-------------------------------------------
Let rate of the current be "c":
Let speed of the boat be "b":
---
Upstream DATA:
time = 5 hrs ; distance = 60 km ; rate = d/t = 60/5 = 12 km/h
-------------------------
Downstream DATA:
time = 3 hrs ; distance = 60 km ; rate = d/t = 60/3 = 20 km/h
--------------------------
Equations:
b-c = 12 km/h
b+c = 20 km/h
--------------------
Add to get:
2b = 32
b = 16 km/h (speed of the boat in still water)
Substitute into b+c = 20 to get c = 4 km/h (speed of the current)
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Cheers,
Stan H.
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