急!F5 more equations 1exq6

44. Cannot figure out its meaning, sorry.
45. Let the speed of the ship = x km/hr.
Speed going down stream = (x + 3)
so time going downstream = 840/(x + 3)
Speed going upstream = (x - 3)
so time going upstream = 840/(x - 3)
840/(x + 3) + 840/(x - 3) = 37.5
112(x - 3) + 112(x + 3) = 5(x + 3)(x - 3)
224x = 5x^2 - 45
5x^2 - 224x - 45 = 0
(x - 45)(5x + 1) = 0, x = - 1/5 (rej.), x = 45.
So time going downstream = time going to town B = 840/(45 + 3) = 17.5 hr.
46.
Let time for tap A to fill the tank alone = x min.
Time for tap B to fill the tank alone = ( x - 25) min.
In 1 min. tap A alone can fill 1/x of the tank
In 1 min. tap B alone can fill 1/(x - 25) of the tank.
Since they can fill up the tank in 30 min., so in 1 min. 1/30 of the tank is filled.
So 1/x + 1/(x - 25) = 1/30
30(x - 25) + 30x = x(x - 25)
60x - 750 = x^2 - 25x
x^2 - 85x + 750 = 0
(x - 75)(x - 10) = 0
x = 10 (rej. because it takes at least 30 min. to fill the tank)
x = 75 min.
So tap A takes 75 min., tap B takes 50 min.