SOLUTION: A boat travels 12 miles up the Mississippi River and 12 miles back down river in a total of eight hours. The rate of the boat in still water is four miles per hour. Find the speed

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Question 347407: A boat travels 12 miles up the Mississippi River and 12 miles back down river in a total of eight hours. The rate of the boat in still water is four miles per hour. Find the speed of the current.
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let speed of current be xmph
downstream speed = x+4 mph
upstream speed = 4-x mph
Time downstream = 12/(x+4)
Time upstream = 12/(4-x)
....
12/(x+4)+12/(4-x)=8
LCD = (x+4)(4-x)
12(4-x)+12(x+4)/(x+4)(4-x)=8
-12x+48+12x+48 = 8(16-x^2)
96=128 8x^2
8x^2=128-96
8x^2=32
x^2=4
x= 2 mph the current speed.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
given:
r%5Bs%5D+=+4 mi/hr
d+=+12 mi
t%5B1%5D+%2B+t%5B2%5D+=+8 hrs
Going upstream:
12+=+%284+-+c%29%2At%5B1%5D
t%5B1%5D+=+12%2F%284-c%29
Going downstream:
12+=+%284+%2B+c%29%2A%288+-+t%5B1%5D%29
12+=+32+%2B+8c+-+4t%5B1%5D+-+c%2At%5B1%5D
By substitution:
12+=+32+%2B+8c+-+%284+%2B+c%29%2A%2812%2F%284+-+c%29%29
-20%2A%284+-+c%29+=+8c%2A%284+-+c%29+-+12%2A%284+%2B+c%29
20c+-+80+=+32c+-+8c%5E2+-+48+-+12c
8c%5E2++=+32
c%5E2+=+4+
c+=+2
The speed of the current is 2 mi/hr
check answer:
Going upstream:
12+=+%284+-+c%29%2At%5B1%5D
12+=+%284+-+2%29%2At%5B1%5D
2t%5B1%5D+=+12
t%5B1%5D+=+6 hrs
Going downstream:
12+=+%284+%2B+c%29%2A%288+-+t%5B1%5D%29
12+=+%284+%2B+2%29%2A%288+-+t%5B1%5D%29
8+-+t%5B1%5D+=+2 hrs
6+%2B+2+=+8 hrs total
OK