The current in a shipping route flows at 4 miles per hour. for a barge to travel 24 miles upriver and returns takes 5 hours. how fast must the barge be able to travel in still water?

Answer 1

24 = (x+4)*t= (x-4)*(5-t)

Xt +4t= 5x -20 -xt+4t

Xt= 5x-20-xt

2xt = 5x-20

T=(5x-20)/(2x)

24= (x+4)(5x-20)/(2x)

48x= 5x^2-80

0= 5x^2-48x-80

X= [ 48 + sqrt ( 2304-1600)]\10

= [ 48 +- sqrt(704)]\10

= [ 48 +- 8*sqrt (11)]/10

=[ 25 +- 4*sqrt(11)]\5

7.653299.... positive branch is only valid solution

Times are 1.1933 and 3.8066....