SOLUTION: A man rows a boat 910 feet upstream against a constant current in 14 minutes. He then rows 525 feet downstream (with the same current) in 7 minutes. Find the speed of the current a
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Question 1007208: A man rows a boat 910 feet upstream against a constant current in 14 minutes. He then rows 525 feet downstream (with the same current) in 7 minutes. Find the speed of the current and the equivalent rate at which he can row in still water.
Found 3 solutions by ankor@dixie-net.com, fractalier, addingup:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A man rows a boat 910 feet upstream against a constant current in 14 minutes.
He then rows 525 feet downstream (with the same current) in 7 minutes.
Find the speed of the current and the equivalent rate at which he can row in still water.
:
let s = rowing speed in still water in ft/min
let c = rate of the current
then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
:
Write a distance equation for each way. Dist = speed * time
:
14(s-c) = 910
7(s+c) = 525
We can greatly simplify these equations, divide the 1st by 17, the 2nd by 7
then use elimination
s - c = 65
s + c = 75
-------------Addition eliminates c find s
2s = 140
s = 140/2
s = 70 ft/min the speed in still water
:
Find the current using s + c = 75
70 + c = 75
c = 75 - 70
c = 5 ft/min the rate of the current
:
:
Confirm this in the 1st original equation
14(70 - 5) = 910
14(65) = 910
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the still water's rate, r.
Call the current's rate, c.
In general, speed is found by dividing distance by time...
So we have two cases...
r - c = 910/14 = 65
r + c = 525/7 = 75
Now add the equations and get
2r = 140
r = 70 feet per minute in still water
which means the current must be
c = 5 feet per minute
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Let speed of rowing be x feet per minute AND speed of current be y feet per minute.
-------------------
Let's remember the formula we need to use, it's the one for distance modified:
Distance= Speed*time Since we want the speed of the current, divide both sides by time:
D/t= S*t/t On the right, t multiplying and t dividing cancel each other and we get:
D/t= S This is the formula we will use, which we derived from D= St
-----------------------------
UPSTREAM
-------------------
x - y ft/minute= Speed upstream
x - y = 910/14
x - y = 65 Add y on both sides:
x = 65+y
---------------------------------------
DOWNSTREAM
----------------------------------------
x + y = 525/7
x + y = 75 Now substitute for x, since we just said that x= 65+y:
65+y+y= 75
2y= 75 - 65
2y= 10 divide both sides by 2:
y= 5 The speed of the current is 5 feet per minute
-------------------------------------
(A) + (B)= 65 + 75= 140
2x = 100
x = 50 ' / minute ANSWER
y = 5' / minute ANSWER
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