Help with this problem

Question

a boat traveled downstream a distance of 90 miles and then came right back. If the speed of the current was 8 mph and the total trip took 6 hours, find the average speed of the boat relative to the water

Answer 1

c= 8 mph, 180 miles in 6 hours, up and back, with and without the current. what is the boat's speed in still water??

d = 90

b + c = d/t

b- c = d/(6-t)

b + 8 = 90/t

b - 8 = 90/(6-t)

subtract

16 = 90/t - 90/(6-t)

multiply by LCD

16(t)(6-t) = 90(6-t) - 90t

96t -16t^2 = 540 -180t

16t^2 -276t +540 = 0

4t^2 - 69t + 135 = 0

factor, complete the square, use quadratic formula or graph the equation

t =15 or 2 1/4

(4t - 9)(t -15)

t = 2.25 downstream, 6-t = 3.25 hours up stream

downstream speed = 90/2.25 = 90/9/4 = 4/9 x 90 = 40 mph

boat speed in still water = 40-8 = 32 mph