SOLUTION: a riverboat for tourists averages 12 mph in still water. It takes the boat 1hour and 4 minutes to go 6 miles upstream and return. find the rate of the current

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Question 766346: a riverboat for tourists averages 12 mph in still water. It takes the boat 1hour and 4 minutes to go 6 miles upstream and return. find the rate of the current
Found 2 solutions by lwsshak3, mananth:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
a riverboat for tourists averages 12 mph in still water. It takes the boat 1hour and 4 minutes to go 6 miles upstream and return. find the rate of the current
***
let c=rate of current
12+c=rate of boat downstream
12-c=rate of boat upstream
1hour and 4 min=1+1/15=(16/15) hour
travel time=distance/rate of speed
6%2F%2812-c%29%2B6%2F%2812%2Bc%29=16%2F15
LCD:(12-c)(12+c)(15)
6(12+c)(15)+6(12-c)(15)=16(12+c)(12-c)
1080+90c+1080-90c=16(144-c^2)
2160=2304-16c^2
16c^2=144
c^2=9
c=±√9
c=±3
c=-3(reject, c>0)
or
c=3
rate of current=3 mph

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let speed of current be x
speed against current = 12-x
speed with current = 12+x
t=d/r
time upstream + time downstream = 1 hour 4 min
6%2F%2812-x%29+%2B+6%2F%2812%2Bx%29=+16%2F15+

LCD = (12+x)(12-x)
6%2812%2Bx%29%2B6%2812-x%29=+%2816%2F15%29%2812%2Bx%29%2812-x%29
72%2B6x%2B72-6x=%2816%2F15%29%28144-x%5E2%29
multiply by 15
144%2A15+=+16%28144-x%5E2%29
/16
9*15=144-x^2
x^2=144-135
x^2=9
x= +/- 3
so x =3 mph the speed of current