it takes bubba the same anount of time to pddle his canoe upstream two miles as it does for him to paddle six miles downstream. if he can manage 2 moh on a lake, how fazt is the current

Answer 1

Let x = the current speed. When you are going upstream, the current is working against you, you would go slower by subtracting, speed in still water - current speed. Downstream is faster so it would be speed in still water + current speed.

Let x = speed of the current

t = d/r

time upstream = time downstream

2/(2-x)=6/(2+x)

To solve, cross multiply

2(2+x)=6(2-x) Distribute

4+2x=12-6x Add 6x to both sides

4+8x=12 Subtract 4 from both sides

8x=8 Divide both sides by 8

x=1 mph is the current speed

Answer 2

speed without current = s

c=current speed

upstream speed = s-c

downstream speed = s+c

distance = speed times time

d=st

t=d/s

t=6/s+c = 2/s-c

the time is the same going 6 miles down stream as 2 miles upstream

6/(s+c) = 2/(s-c)

3/(s+c) = s-c

3 = s^2 - c^2

If s=2, the speed on a lake with no current

then 3 = 2^2 - c^2

3 =4-c^2

c^2 = 1

c = 1 mph

he goes 2+1=3 mph downstream

he goes 2-1= 1 mph upstream

downstream takes 2 hours going 3mph so it's less than an hour d=st d= 3x2 = 6 miles

upstream takes 6 hours going 1 mph so d=1x2 hours = 2 miles