Raymond B. answered • 05/14/22
Math, microeconomics or criminal justice
3 mph = r = rate of speed of the dog in still water
c = the stream speed
10 miles = distance one way, 20 miles = total distance down and back
12 hours = total time upstream and downstream
t= time upstream
12-t = time downstream
d=st
10 = (3+c)(12-t) = 36 +12c -3t -ct
10 = (3-c)t = 3t -ct
36+12c -6t = 0
6+2c -t = 0
t =6+2c
10 = (3-c)(6+2c)
10 = 18 -2c^2
5 = 9-c^2
c^2 =4
c = 2 mph = current speed
or if you interpret the problem differently with 12 hours as only the upstream time, then
3 mph in still water =r = rate of speed of the dog in still water
10 miles downstream= same distance upstream = d
12 hours upstream,= time t, at r-c mph
how fast is the current, c?
distance = net speed times time traveled
d = st, s=r-c upstream net speed
10 miles = upstream speed times 12 hours
10 = (r-c)12
10 =(3-c)12
10 =36-12c
12c =36-10 =26
c =26/12 = 2 1/6 mph = current speed
c= about 2 mph
D=2 is the "best" answer or closest to the actual answer
either interpretation and D is the answer
d = (r+c)t r=rate of speed in still water, c = current speed, t = time traveled
downstream where T= time traveld downstream
10=(r+c)T
10=(3+ 2 1/6)T
10 =(5 1/6)T
T = 10/(31/6) = 60/31
T = 1 29/31
T = about 1.94 hours downstream = about 1 hour and 56 minutes
T = about 2 hours downstream = about 6 times as fast as 12 hours upstream
5 1/6 is about 6 times as fast as 3- 2 1/6 = 5/6 mph upstream
