the rate of the current in the susanna river is 4km/h. if the canoeist can paddle 5km downstream in the same amount of time she can paddle 1km upstream, how fast can she paddle in still water?
please show how you got your answer!
2007-04-02 14:51:46 · 7 answers · asked by tropicaltwist782 5 in Science & Mathematics ➔ Mathematics
Let velocity of paddler=x
Then, in any trip, velocity x time = distance.
Going downstream (4+x) T = 5 and
going upstream (x-4) T = 1
Then 4T + xT = 5
xT - 4T = 1
Subtracting, 8T = 4, T = 1/2 and x=6 km/hr
2007-04-02 14:59:48 · answer #1 · answered by cattbarf 7 · 1⤊ 0⤋
speed : distance / time
time: distance/speed
distance : speed * time
upstream speed : still water speed - current speed
downstream speed : still water speed + current speed
let x : still water speed in kmph
then upstream speed in kmph : x - 4
then downstream speed in kmph : x + 4
so knowing time = distance/speed, the equation would be
5 / (x + 4) for downstream
1 / (x - 4) for upstream
since they're equal:
5 / (x + 4) = 1 / (x - 4)
to solve for x, cross multiply:
5 (x - 4) = 1 (x + 4)
distribute:
5x - 5*4 = 1*x + 1*4
5x - 20 = x + 4
subtract x from both sides:
5x - x - 20 = x - x + 4
4x - 20 = 4
add 20 to both sides:
4x - 20 + 20 = 4 + 20
4x = 24
divide both sides by 4 to get x:
4x/4 = 24/4
x = 6
so susanna's speed in still water is 6 km per hour
2007-04-02 22:11:25 · answer #2 · answered by rooster1981 4 · 1⤊ 0⤋
Hmm.
5km(X-4)=1km(X+4)
5kmX-20km=1kmX+4km
+20km +20km
5kmX=1kmX+24km
-1kmX -1kmX
4kmX=24km
X=6km
That is my guess.
2007-04-02 22:00:30 · answer #3 · answered by Anonymous · 1⤊ 0⤋
t=d/s
downstream
here,
speed of stream will be added to speed in still water
t=5/x+4
upstream
here,
speed of stream will be subtracted from speed in still water
t=1/x-4
t is same in both cases
therefore
1/x-4=5/x+4
x+4=5x-20
4x=24
x=6km/h (speed in still water)
2007-04-02 22:03:16 · answer #4 · answered by mathiphy 2 · 1⤊ 0⤋
Sit next to the smart kid tomorrow.
2007-04-02 21:59:30 · answer #5 · answered by Anonymous · 0⤊ 2⤋
i'm siiiik of algebra. thank GOD were on our skool break!!
2007-04-02 21:54:43 · answer #6 · answered by Anonymous · 0⤊ 0⤋
my answer came to: Do your own damn homework!
2007-04-02 21:54:06 · answer #7 · answered by Anonymous · 1⤊ 3⤋