The current of a river is 3 miles per hour. A boat travels to a point 176 miles upstream and 176 miles back in 19 hours. What is the speed of the boat to the nearest tenth in water without a current?

Answer 1

176 miles up and back for total 352 miles in 19 hours with a current of 3 mph

d=rt

distance = rate of speed times time

176= (b+c)x= (b-c)(19-x) where x= time downstream, 19-x = time upstream

c=3 mph= current speed, b= boat speed in still water

176/x =b+3

176/(19-x)=b-3

subtract

176/x - 176/(19-x)=6

88/x-88/(19-x)=3

88(19-x)-88x=3x(19-x)

19(88)-88x-88x= 57x-3x^2

3x^2-229x+1672=0

x=229/6+/-(1/6)sqr(229^2-12(1672))

=(229+/-179.936)/6

= 8.177 hours or 68.156 hours

b=176/x-3= 176/8.177 -3 or 176/68.156 - 3

b = 10.524 mph (ignore the negative solution)

boat speed in still water is about 10.5 mph