Question

The time required for a trip 108 miles downstream on a steamer is 3 hours less than the time required for the upstream trip. A boat whose rate is 6 miles per hour less than that of the steamer required 9 hours more for the upstream trip than for the downstream trip. Find the rate of the stream.

PLZ HELP Thank you!

Answer 1

let speed of steamer in still water be x mph
let the speed of the current be y mph
108/(x-y) - 108/(x+y) = 3
108x + 108y - 108x + 108y = 3(x^2 - y^2)
216y = 3(x^2 - y^2)
72y = x^2 - y^2 ---- #1

let speed of "boat" be x-6
108/(x-6 - y) - 108/(x-6 + y) = 9
108x - 648 + 108y - 108x + 648 + 108y = 9(x^2+xy-6x-xy-y^2+6y-6x-6y+36

216y = 9(x^2 - 12x - y^2 + 36)
24y = x^2 - y^2 - 12x + 36
x^2 - y^2 = 12x + 24y - 36 ---- #2

then 12x + 24y - 36 = 72y
12x - 48y = 36
x - 4y = 3
x = 4y + 3

sub into #1

x^2 - y^2 - 72y = 0
(4y+3)^2 - y^2 - 72y = 0
16y^2 + 24y + 9 - y^2 - 72y = 0
15y^2 - 48y + 9 = 0
5y^2 - 16y + 3 = 0
(5y + 1)(y - 3) = 0
y = -1/5 , not possible
or
y = 3 mph

the current has a speed of 3 mph